One of God’s favorite individuals throughout the Bible was Abraham. Abraham showed exceptional faith towards God and a promise of a continued loyalty to God. For this, God blesses Abraham. The specific blessing was that Abraham’s descendants would bless the world:

Gen 22:18 In your seed all the nations of the earth shall be blessed, because you have obeyed My voice.”

And,

Gen 26:4 And I will make your descendants multiply as the stars of heaven; I will give to your descendants all these lands; and in your seed all the nations of the earth shall be blessed;

God’s particular method under which Abraham’s descendants would bless the world was to create them into a chosen people under whom the rest of the world would be proselytized. In Exodus, God explains this to Israel:

Exo 19:5 Now therefore, if you will indeed obey My voice and keep My covenant, then you shall be a special treasure to Me above all people; for all the earth is Mine.
Exo 19:6 And you shall be to Me a kingdom of priests and a holy nation.’ These are the words which you shall speak to the children of Israel.”

Note that this is all conditional. Because Abraham was faithful, his progeny were chosen to be priests. In this verse, as long as those individuals remain faithful, God will grant them this special privilege. If they strayed, God had latitude to revoke His promise.

God chose Israel to be a priest nation, one which would evangelize the world. For this reason God gave them the law and created a special bond with them, such that the entire would could become God-fearers:

Deu 4:5 “Surely I have taught you statutes and judgments, just as the LORD my God commanded me, that you should act according to them in the land which you go to possess.
Deu 4:6 Therefore be careful to observe them; for this is your wisdom and your understanding in the sight of the peoples who will hear all these statutes, and say, ‘Surely this great nation is a wise and understanding people.’
Deu 4:7 “For what great nation is there that has God so near to it, as the LORD our God is to us, for whatever reason we may call upon Him?

This theme is a prominent subtheme in the Bible, masked by the major theme of God trying to just capture the loyalty of His chosen people. One cannot begin to proselytize without first having a core of people able to proselytize. In Isaiah, the prophet waxes hopeful that Israel would finally become that light to the world:

Isa 42:6 “I, the LORD, have called You in righteousness, And will hold Your hand; I will keep You and give You as a covenant to the people, As a light to the Gentiles,
Isa 42:7 To open blind eyes, To bring out prisoners from the prison, Those who sit in darkness from the prison house.

In Isaiah 42, Israel was stated to bring freedom from darkness to the gentiles. This is obviously figurative. Israel was not called to build electric lights or lockpicking sets. Israel was called to proselytize for God.

Isa 49:6 Indeed He says, ‘It is too small a thing that You should be My Servant To raise up the tribes of Jacob, And to restore the preserved ones of Israel; I will also give You as a light to the Gentiles, That You should be My salvation to the ends of the earth.’ “

In Isaiah 49, God states that He will use Israel to bring salvation to the “ends of the earth”. This salvation consisted of peace, justice, and prosperity. See Isaiah 42:1 and Isaiah 61:5:

Isa 42:1 “Behold! My Servant whom I uphold, My Elect One in whom My soul delights! I have put My Spirit upon Him; He will bring forth justice to the Gentiles.

And,

Isa 61:5 Strangers shall stand and feed your flocks, And the sons of the foreigner Shall be your plowmen and your vinedressers.
Isa 61:6 But you shall be named the priests of the LORD, They shall call you the servants of our God. You shall eat the riches of the Gentiles, And in their glory you shall boast.
Isa 61:7 Instead of your shame you shall have double honor, And instead of confusion they shall rejoice in their portion. Therefore in their land they shall possess double; Everlasting joy shall be theirs.

Isaiah 61 is probably referring to the prosperity of the priests to whom the Gentiles bring offerings, but the land is depicted as peaceful and prosperous in order to make this happen. This coincides with another Biblical theme that nations who serve God are blessed materially.

The Psalms echo this same subtheme:

Psa 67:2 That Your way may be known on earth, Your salvation among all nations.
Psa 67:3 Let the peoples praise You, O God; Let all the peoples praise You.
Psa 67:4 Oh, let the nations be glad and sing for joy! For You shall judge the people righteously, And govern the nations on earth. Selah
Psa 67:5 Let the peoples praise You, O God; Let all the peoples praise You.

And,

Psa 98:2 The LORD has made known His salvation; His righteousness He has revealed in the sight of the nations.
Psa 98:3 He has remembered His mercy and His faithfulness to the house of Israel; All the ends of the earth have seen the salvation of our God.
Psa 98:4 Shout joyfully to the LORD, all the earth; Break forth in song, rejoice, and sing praises.
…
Psa 98:9 For He is coming to judge the earth. With righteousness He shall judge the world, And the peoples with equity.

And,

Psa 117:1 Praise the LORD, all you Gentiles! Laud Him, all you peoples!
Psa 117:2 For His merciful kindness is great toward us, And the truth of the LORD endures forever. Praise the LORD!

God’s goal is to reach the entire world. This is an enduring goal and is repeated throughout the Bible. This theme possibly extends into the New Testament (Mat 28:19, Mar 16:15). Note that there is no indication of full acceptance of Gentiles as equal to Jews until the arrival of Paul (Rom 10:12). Before Paul, Gentiles had to become Jews in order to be equal to Jews. God accepted these Gentiles precisely because He was building a priest nation. If an individual desired God enough to partake in the law, that granted entrance into the body of Israel.

We see this first described in Exodus. In Exodus, the Jews have finally become a nation and soon deal with their first converts. A host of gentiles exit Egypt under the protection of Israel:

Exo 12:37 Then the children of Israel journeyed from Rameses to Succoth, about six hundred thousand men on foot, besides children.
Exo 12:38 A mixed multitude went up with them also, and flocks and herds—a great deal of livestock.

These Gentiles were allowed Israelite status by keeping to ordinances handed down by Moses, ordinances which they were present to receive at Mount Sinai:

Exo 12:48 And when a stranger dwells with you and wants to keep the Passover to the LORD, let all his males be circumcised, and then let him come near and keep it; and he shall be as a native of the land. For no uncircumcised person shall eat it.
Exo 12:49 One law shall be for the native-born and for the stranger who dwells among you.”

This is echoed elsewhere:

Isa 56:3 Do not let the son of the foreigner Who has joined himself to the LORD Speak, saying, “The LORD has utterly separated me from His people”; Nor let the eunuch say, “Here I am, a dry tree.”
Isa 56:4 For thus says the LORD: “To the eunuchs who keep My Sabbaths, And choose what pleases Me, And hold fast My covenant,
Isa 56:5 Even to them I will give in My house And within My walls a place and a name Better than that of sons and daughters; I will give them an everlasting name That shall not be cut off.
Isa 56:6 “Also the sons of the foreigner Who join themselves to the LORD, to serve Him, And to love the name of the LORD, to be His servants— Everyone who keeps from defiling the Sabbath, And holds fast My covenant—
Isa 56:7 Even them I will bring to My holy mountain, And make them joyful in My house of prayer. Their burnt offerings and their sacrifices Will be accepted on My altar; For My house shall be called a house of prayer for all nations.”
Isa 56:8 The Lord GOD, who gathers the outcasts of Israel, says, “Yet I will gather to him Others besides those who are gathered to him.”

In Isaiah, God is said to accept all who serve God (although in Deuteronomy 23 God imposes some limitation based on national tensions). Verse 7 even uses the acceptance of these Gentiles as a foreshadowing of the proselytization of all nations. All the Gentiles had to do was follow the law. A fleeting reference to this can also be found in Nehemiah:

Neh 10:28 Now the rest of the people—the priests, the Levites, the gatekeepers, the singers, the Nethinim, and all those who had separated themselves from the peoples of the lands to the Law of God, their wives, their sons, and their daughters, everyone who had knowledge and understanding—

At the time of Nehemiah, there was a large contingent of foreigners who served God. This seems to have been a constant in the history of Israel, so much so that the Roman author Cassius Dio records:

They have also another name that has been acquired,–i.e., the country has been called Judaea, and the people themselves Jews. I do not know from what source this title was first given them, but it applies also to all the rest of mankind, although of foreign race, who cherish their customs.

In Isaiah 66, the prophet even extends the priesthood status (even the Levite status) to some of these foreigners:

Isa 66:18 “For I know their works and their thoughts. It shall be that I will gather all nations and tongues; and they shall come and see My glory.
Isa 66:19 I will set a sign among them; and those among them who escape I will send to the nations: to Tarshish and Pul and Lud, who draw the bow, and Tubal and Javan, to the coastlands afar off who have not heard My fame nor seen My glory. And they shall declare My glory among the Gentiles.
Isa 66:20 Then they shall bring all your brethren for an offering to the LORD out of all nations, on horses and in chariots and in litters, on mules and on camels, to My holy mountain Jerusalem,” says the LORD, “as the children of Israel bring an offering in a clean vessel into the house of the LORD.
Isa 66:21 And I will also take some of them for priests and Levites,” says the LORD.

One theme of the Bible is that Israel was chosen as a priest nation by benefit of being descended from Abraham. Throughout the Bible God attempts to mold them into a priest nation, who was then to proselytize the world. In this way, the entire world would have fellowship with God. God was not just singularly concerned only with Israel, but sought to use them as a vessel to reach all mankind. As such, God built in conditions by which foreigners could become grafted into His chosen people and serve as priests to the rest of the world. God even promises some Gentiles the coveted status of Levitical priesthood. Such was God’s plans for Israel, His end purpose, and His acceptance of the Gentiles.