The Noahide laws were given to the non-Jewish nations both past and present to follow and do them. This was predicated on the fact that the non-Jewish nations must acknowledge the fact that HaShem gave these laws-instruction manual to us Jews as part of the Torah.
“Moses began his blessing by praising the Jewish people for accepting the Torah unconditionally. He contrasted the Jews’ acceptance of the Torah with the other nations’ refusal to accept it, when G‑d offered it to them before giving it to the Jews.
[Moses] said, “G‑d came from Sinai [to give the Jews the Torah], shining forth to them from [Mount Sei’ir, after offering the Torah to the Edomites]; He appeared [to the Jews] from Mount Paran [where He had offered the Torah to the Ishmaelites].” Deuteronomy 33:2
The Edomites and Ishmaelites represent all non-Jewish nations, past and present. By offering the Torah to the non-Jewish nations, G‑d rendered them receptive to later accepting their obligation to observe the “Noahide” laws. These are the seven categories of commandments that must be observed by all non-Jews. In order to properly accept this legal code, the non-Jew must acknowledge that G‑d gave it to humanity as part of the Torah that He gave at Mount Sinai.
Furthermore, in the Messianic future, the non-Jewish nations will be refined and no longer oppose the lifestyle and world-vision of the Torah. By approaching the nations of the world with the option to accept the entire Torah, G‑d implanted within them the receptivity to both their present obligation to accept the Torah’s authority over them – obligating them in the Noahide laws – as well as their future acceptance of the Torah’s world-vision, transforming them into active participants in the final Redemption.1 Hitva’aduyot 5742, vol. 1, pp. 223–224; Hitva’aduyot 5748, vol. 1, p. 92.