To me, this was interesting because even where they are a native species, the puma is solitary, ellusive, range very widely and find it very easy to avoid contact with humans.
Yes, the US is huge compared to the UK, and has vasts expanses of forest and other wilderness areas - but also, conservation, outdoor activities, and in particular, hunting are very big. These sorts of activities would / shoud bring people into contact with cats, in the same way that is argued for the UK. The reality is that this species is adept at keeping iteslf to itself...
ETA -
whilst I'm sure there's the odd escaped big cat prowling around, I don't see how there can be enough of them to have a breeding population,
Looking at the wikipedia entry for the puma, they are attributed with being able to maintain a breeding population based on very low and widely dispersed populations.
Think about it - for a solitary creature that lives and hunts alone and by stealth, it's pretty much a given that they need to be able to hook up with each other even over the large territories that they roam. Scent marking etc I guess.