please just learn Daf 68a in Shabbos with Tosfos and learn about the case about a convert who converted in a city of non-jews and somehow never learned about shabbos and it is still a kosher conversion.
Besides that fact I know many modern orthodox jews hat never covered their hair in the first place and that is the way these people were raised in their communities. Leave Brooklyn and go to modern orthodox communities in south or west and even some communities in New jersey and Queens a majority of the Jewish women do not cover their and they may even wear pants. I’m not saying I agree with what they do but this is a fact and these people in all other respects are orthdox jews and they believe that they are orthdox jews.
So please stop this idea of assuming if a women doesn’t cover her hair it makes her a questionable convert because it doesn’t. Also it is not one of the 613 mitzvos to cover her hair and it is only a das yehudis and has a lot more to do with then just tziyus. Because if a girl covered her hair only for tziyus reasons unmarried women would have cover their hair and shetels would be a problem.