Yes you can build a house solo although it will take some time to get to that point but theres plenty of out of the way places that the larger groups aren't interested in because of the limited open areas that they need.
Yes you can build on a homestead - homesteads are tribes for 1-4 people. You are limited in room so to get your architecture skill up you might have to build, dismantle, and build again.
There are also some other things to take into consideration - personally I made sure to take fishing so I could feed myself easily. If you are truly going to try and solo you want to make sure to find some suppliers in your area early on because having baskets and tools available makes life so much easier.