How long does a group have to live somewhere to be indigenous?

Well if you think that native Americans are an indigenous culture to North America then that would be incorrect because they descended from ancient paleo Siberian’s ( in fact some DNA evidence suggests they may also have been European... https://www.science.org/content/article/scienceshot-native-americans-were-mix-asian-and-european ) so they aren’t indigenous either according to your metric. You see how silly your hypothesis is?

As someone said, your understanding of culture isn’t very well developed or cogent. Just stop with the silly indigenous stuff, cultural osmosis is a thing and there is no ‘definitive’ culture in any given area on earth. It’s all a constant adaptation to and amalgamation of various cultures intermingling over time. A future civilization discovering a US president and describing it as an ancient American would be entirely true relative to the time period from when they discover it.