You don’t need to be in the USA unless you’re taking out a loan with them. If you are using a different form of payment it’s quite easy to do it all from the UK.
Edited to add: mine was a couple of years ago but I had to sign physical contracts, rather than resale which I did digitally. They sent them quite quickly via FedEx and provided a number for me to arrange for them to be collected from my house. I’m not sure if they can be done via email yet.