Before Avraham, we see that many Non-[officially]-Jews [Kain, Abel,Noah, Shem] built stages/altars for offerings to G-d.
From then, through the periods of the Temples and nowadays, when were the Non-Jews allowed to build stages/altars (במות/מזבחות) to offer their sacrifices to [one, our] G-d? And are they allowed to do that today?
Yes. Non-Jews may sacrifice to G-d on any private altar they build, anywhere in the world.
Rambam Hilchot Ma'aseh HaKorbanot 19:16:
וְהַנָּכְרִים מֻתָּרִין לְהַקְרִיב עוֹלוֹת לַשֵּׁם בְּכָל מָקוֹם. וְהוּא שֶׁיַּקְרִיבוּ בְּבָמָה שֶׁיִּבְנוּ.
Non-Jews may offer burnt offerings to G-d in any place, offering them on an altar which they have built.
