It means a long time into the 20th century, in this sentence/context it would be close to the middle or later 1950 or later

If something is "in doubt", it means people are not certain about it. So, if "the identity of the Maoi builders" is in doubt, it means people are not sure who the Maoi builders were. ("Identity" means who a person is). "Until well into the 20th century". The "well" in this context means "far". So the whole sentence means "People were unsure who the Maoi builders were, until we were far into the 20th century". Hope that helps!