A friend of mine was making $20 an hour at a part time manufacturing job while he had classes, and full time plus overtime during breaks. It would have been plenty for a down payment on such a house, if he'd wanted to, but he put the money towards tuition to limit school loans instead. This was 20 years ago, give or take, so very much not the norm, but definitely possible.

To add: I think a minimum down payment for the mortgage probably would have been in the $4 or $5,000 range.