Gal 3:8, Mt 8:11, Acts 13:47-48, Acts 15:15-18, Rom 15:9-12, Rev 7:9-10
In the Old Testament, God said that on that day many Gentiles would return to God. (Zec 8:20-23)
Zec 8:20 Thus saith the Lord of hosts; It shall yet come to pass, that there shall come people, and the inhabitants of many cities: 21 And the inhabitants of one city shall go to another, saying, Let us go speedily to pray before the Lord, and to seek the Lord of hosts: I will go also. 22 Yea, many people and strong nations shall come to seek the Lord of hosts in Jerusalem, and to pray before the Lord. 23 Thus saith the Lord of hosts; In those days it shall come to pass, that ten men shall take hold out of all languages of the nations, even shall take hold of the skirt of him that is a Jew, saying, We will go with you: for we have heard that God is with you.
God first preached the gospel of justification by faith to Abraham and told Abraham that the Gentiles would be saved through faith just like Abraham. (Ga 3:8)
Ga 3:8 And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed.
Jesus also said that many Gentiles would be saved. (Mt 8:11)
Mt 8:11 And I say unto you, That many shall come from the east and west, and shall sit down with Abraham, and Isaac, and Jacob, in the kingdom of heaven.
When the Gentiles heard the gospel that Jesus was the Christ, they were saved by believing in it. (Acts 13:47-48)
Acts 13:47 For so hath the Lord commanded us, saying, I have set thee to be a light of the Gentiles, that thou shouldest be for salvation unto the ends of the earth. 48 And when the Gentiles heard this, they were glad, and glorified the word of the Lord: and as many as were ordained to eternal life believed.
According to the prophecies of the Old Testament prophets, the Gentiles sought God and were saved by believing in Jesus as the Christ. (Acts 15:15-18, Romans 15:9-12)
Acts 15:15 And to this agree the words of the prophets; as it is written, 16 After this I will return, and will build again the tabernacle of David, which is fallen down; and I will build again the ruins thereof, and I will set it up: 17 That the residue of men might seek after the Lord, and all the Gentiles, upon whom my name is called, saith the Lord, who doeth all these things. 18 Known unto God are all his works from the beginning of the world.
Romans 15:9 And that the Gentiles might glorify God for his mercy; as it is written, For this cause I will confess to thee among the Gentiles, and sing unto thy name. 10 And again he saith, Rejoice, ye Gentiles, with his people. 11 And again, Praise the Lord, all ye Gentiles; and laud him, all ye people. 12 And again, Esaias saith, There shall be a root of Jesse, and he that shall rise to reign over the Gentiles; in him shall the Gentiles trust.
In the future, the peoples of each nation will be saved and will praise God and Christ. (Rev 7:9-10)
Rev 7:9 After this I beheld, and, lo, a great multitude, which no man could number, of all nations, and kindreds, and people, and tongues, stood before the throne, and before the Lamb, clothed with white robes, and palms in their hands; 10 And cried with a loud voice, saying, Salvation to our God which sitteth upon the throne, and unto the Lamb.