So then God would decide if a male would be approved by God and not by men if a Gentile man doesn't get circumcized. Would the group (or sect) you belong to accept an uncircumcized male as a convert to Judaism?
I don't belong to a sect or a group. If a non-Jew were to decide that they want to take on the Torah that was given and Mount Sinai, as Hashem gave it, and also connect himself / herself to the Jewish people the way it has been done for thousands of years by others who successfully did so, then in many Torah based / Orthodox Jewish communities there is a path for that.
Because Hashem gave a mitzvah to Torah based Jews, which we call Brith Milah for males, of course any potential convert to Torath Mosheh would have use Avraham ben-Terahh as his / her example to do so. Thus, of course before they complete the conversion process they would need to undergo a Brith Milah.
Because there is no requirement for the non-Jewish world to become Jewish, there is no requirement for a non-Jew to seek that out lness they compelled themselves to take up the path of Torah.