I assume you are talking about the contiguous 48, and a USA similar to the one in OTL. Anyone could create an AH in which the US is so weak, so divided, or so different from OTL that this could happen.
So we are talking about "our" USA, right? Anytime prior to the 1950's it would be fairly easy for a foreign power to invade and occupy (at least for a very short time) parts of Hawaii, Alaska. Regarding the contiguous 48, the only way in the 20th century a non-American power could sucessfully invade the US and stay for a while would be through Canada or Mexico, and then you have to presume some pretty odd things have happened in those places. I just don't see a successful seaborne or airborne invasion directly to the US working, period.
If I had to create a scenario, it might involve some way that Mexico gets allied (officially or unofficially) with someone like Germany or Japan in the early 20th century without invoking a US invasion right off the bat. Unlikely, but perhaps possible if the Mexicans and their allies are very, very careful, and the US undergoes an earlier transition away from Monroe Doctrine imperialism. Perhaps, after several decades of a gradual influx of (let's say German) military advisors, technicians, etc without any obvious threats to the US, the US lets its guard down and the Germans begin to build up military forces in Mexico, perhaps under the pretext of assisting Mexico in keeping Mayan rebellions in Yucatan or whatever under control. Create some multiple diversions making the US look elsewhere in the world at the critical time and the evil Krauts start a war, their forces and their Mexican puppets attack the SW USA, and the US cannot respond as effectively as it would like. The invasion would eventually be defeated, probably sooner rather than later, but the image of the Texas capitol dome in flames while Jackbooted forces of the Kaiser march into Austin is pretty darned irresistable.