God did distinguish the Israelites by setting them apart as his own nation (Lev 20:24-26), yet his reason for doing so was not to play favorites, but to benefit everyone (Gen 18:18, 22:18). The Israelites were intended to be an example to others, so that everyone would hear about God and be saved. When other nations witnessed or heard about Israel's history - that is, their relationship with God and God's actions on their behalf - those nations would hear about God and have reason to believe in him. God performed the miracles in Egypt and during the Exodus for this reason (Ex 9:16, Josh 4:23-24), and they did cause people in other nations to revere God (Josh 2:8-11).
Throughout the Old Testament there are pointers to God's global vision. The Psalms often refer to God as the God of all nations (Ps 47:8-9, 99:2) They prophesy that all nations will worship God (Ps 86:9) and call on them to worship him in the present (Ps 47:1, 117:1). Other Psalms speak of God revealing himself to all nations (Ps 98:2, Ps 67), through his deeds and through the Israelites praising him to other nations (Ps 9:11, 96:3, 10, 105:1). Several passages in Isaiah also talk about God's plans to include the Gentiles (42:6, 56:7, 66:19), especially 49:6:
"It is too small a thing for you to be my servant to restore the tribes of Jacob and bring back those of Israel I have kept. I will also make you a light for the Gentiles, that you may bring my salvation to the ends of the earth."
The Apostle Paul used similar verses to illustrate this in Romans 15:8-12.
The laws given to the Israelites were also meant to get the world's attention (Dt 4:6) and included several provisions for Gentiles. God loved the Gentiles and provided for them (Dt 10:18), and instructed the Israelites to love foreigners as themselves (Lev 19:33-34, Dt 10:19), particularly because they had been foreigners in Egypt. This included providing for needy immigrants (Lev 23:22, Dt 24:19-22) and not mistreating or oppressing them (Ex 23:9, Dt 24:14-15, 17-18, Dt 27:19) but treating them equally under the law (Num 15:15-16, Lev 24:22). Those who became followers of God would be Israelites in God's view (Jer 12:16) and could participate in Passover (Ex 12:48-49).