Yes, it's possible to DIY a home. Having a second person will more than double your speed, though. It's a lot of work.
In fact, it's on my bucket list when I retire--build our perfectly-designed retirement home on the perfect lot in the perfect, low-tax state...
As far as "alternatives to buying a home", there are plenty. Travel and live in an RV. Cruises. Log cabins. Move in with kids. Homes built with double walls for extra insulation, or SIP, or ICF. There's someone in the DIY category who is finishing a 2-car garage into a full home for their family.