Hey there! Do you have some more context of a source for this question?

As is, there's not much to answer beyond "No." In 1200 BC, the world was more or less populated as it is today. Your hypothesis would require every single population to have mixed completely with Levantine settlers, or their descendants. The odds of not a single purely native population existing anywhere in the world are incredibly low, especially considering "uncontacted" people groups and that Eurasian-American mingling only occurred with any frequency just 500 years ago.