Is financing a single-family house feasible for us?

But probably EVERYONE had a little shock moment after moving out of their parents' house. We all thought that we basically already bought everything ourselves in the end and that the expenses would stay the same.

I'll just jump in here and ask the simple question: why do you need a basement? The washing machine is better upstairs, near the clothes. Supplies can be stored in a tall cabinet in the kitchen. Hobby equipment can be stored in niches and well-planned storage space. Gladly also under the ceiling (ideal for surfboards, for example). The party in the party basement has been over for X years. It can also take place at the dining table and anyway ends up in the kitchen. There is simply no very good reason for a basement, except for a hillside location.

Could one not build a garage (if very much desired) with a storage room on a hillside? Then you have one more room and a garage and no social housing

The actually planned garage also includes a larger storage room. Actually intended for bicycles and garden tools.

Without a basement might be a matter of habit or lifestyle. Our parents' basements are not empty despite large living space.
But maybe it would be an option to only have the garage with a basement.

But saying "getting by" is really a massive understatement. You can also get by on [Hartz4]. Entitlement...