Are there Old Testament Scriptures that indicate the God of Abraham and Moses (the Jewish God) would reach out to the Gentile (non-Jewish) nations?


Yes! There are numerous Scriptures in the Old Testament declaring that God was going to send a Savior who also would reach out to the Gentiles (or all nations). Let's take a look at a New Testament section of Scripture that quotes many Old Testament Scriptures.
For I tell you that Christ has become a servant of the Jews on behalf of God's truth, to confirm the promises made to the patriarchs so that the Gentiles may glorify God for his mercy, as it is written: "Therefore I will praise you among the Gentiles; I will sing hymns to your name" (quote from Ps. 18:49).

Again, it says, "Rejoice, O Gentiles, with his people" (quote from Deut. 32:43). And again, "Praise the Lord, all you Gentiles, and sing praises to him, all you peoples" (quote from Psalms 117:1). And again, Isaiah says, "The Root of Jesse will spring up, one who will arise to rule over the nations; the Gentiles will hope in him" (quote from Isa. 11:10).
(Rom. 15:8-12)
All of these Scriptures are excellent. Allow me to emphasize two of them.

Notice how verse ten, which is a quote of Deuteronomy 32:43, declares that the Gentiles and God's current people at that time (the Jewish nation) would rejoice before God together.

Also, notice how verse 12 declares that the Gentiles would hope in the God of the Jewish people, through the Root of Jesse, whom I'm convinced is Jesus. God's intention has always been to save all people through a common savior, Jesus.

"For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life" (John 3:16).

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