Is it more difficult to score a Tenure Track position in the US when applying from outside?

While the "I don't know your university" element can have an influence on whether your application gets summarily dismissed to the reject pile, it's less of an issue than one might think. We all travel to Europe and Asia for conferences now, and meet colleagues who come from different countries. I can probably name the top few universities in my field in many European countries, as well as personally know people in each of them.

But there's a more mundane logistical reason for potentially avoiding applicants from other countries: expenses. There's always a risk in getting someone to come for an on-site interview, but with a foreign candidate the expense and logistical work (visa processing, payment methods and so on) are more onerous. We always want to find strong candidates, but when there's a large pool of highly qualified candidates in the US, it can be convenient to focus on those that we expect have a chance of actually making it through the interview process and coming.

There's also the question of whether someone from Europe (as opposed to someone working there) really does want to come to the US, or is just casting a wide net. But that can be addressed in candidate statements or even conversations.

None of this means that foreign candidates are disqualified. Far from it. But it creates a moment of doubt.

I'm going to speak out of personal experience. I did my PhD in Japan, and then started doing a Postdoc in the US, my University in Japan is regarded in most rankings as a better institution that my current one in the US (not by much, but still).

I applied roughly to the same number of postdocs while in Japan and now, that I'm changing gigs as well. In Japan I got only 3 replies. While now I got many more replies and much more requests for interview.

So there's that to that. I'm also Mexican, with a valid travel visa (yes, they asked that), so we as part of NAFTA can get relatively easy working Visas (we only need a letter of acceptance). Also, a trip from Mexico City to LA is cheaper/shorter than a trip from Washington to LA

I think our experiences have many differences, but in my personal point of view, yes it is easier to get positions if you are already in the US.

Also, to be blunt, few people in the US are going to take you seriously if you do not have at least a postdoc (in whatever institution). Even James Watson (Nobel Prize Laureate) did a Postdoc.