Is it ever possible to finance a house?

Well, I wouldn’t see it quite that badly. First of all, the OP doesn’t want to build/buy a house now, but only when she goes back to work. Whether that is part-time or full-time is still up in the air. Of course, one should always plan for the possibility of being the sole earner for a certain period, whether due to unemployment or, for example, because there is no daycare place immediately available after parental leave. But assuming that a woman will not work at all anymore is a bit exaggerated. I think your acquaintance could certainly take a new job at another company in the foreseeable future, even if she quit because of the untenable working conditions, at least part-time, if she wanted to. So this argument doesn’t really hold up.

If there are no exceptional reasons (e.g. health issues) with the mother or child, or the desire to stay at home (if financially feasible) that would speak against a job and the associated income, then one can expect to earn at least part of the previous income. If that were not the case, most families would not be able to build or buy a house. By the way, I personally don’t know a single woman (and I know many mothers) who did not return to work after parental leave or quit shortly after. What I do know, however, are mothers who after a short time opted for a part-time job, even though they originally wanted to go back to work full-time.