Is home financing possible like this? Alternatively, save equity for a few years

I think more like 310k, because from the 40k equity to be used, the incidental purchase costs still need to be deducted.

Exactly. We would need a loan of 306,500 (346,500 total price - 40,000 equity) to be precise.

It's somehow a tough decision. I do think that it would currently be feasible. However, in 3 years, with almost 70,000 more equity and maybe only slightly higher interest/construction costs (you would also get a better nominal interest rate through a higher equity share), it would already look significantly more comfortable in terms of the monthly rate. Of course, it is perfectly possible to go the other way as well.

please read the OP's post again, take it into account, and don't come up with incorrect numbers. This is not about your situation, but about the OP's.

in which other direction should it go? That interest rates have risen sharply in three years? That is reading from a crystal ball. In such a favorable situation as you have now, very few can live almost rent-free and save properly. How many can already save 1800 euros per month? If interest rates rise so much that 1800 euros per month are not worthwhile, then we have a completely different problem here in Germany.

It's kind of a hard decision

Because it's a pretty close call. €306,500 isn't exactly dirt cheap thanks to the high loan-to-value, so the €1,100 installment is tight... I'd talk it over with financial advisors again

You can also put the 1800 into a [Bausparvertrag] and thus secure the low interest rate.

I find all those who shout "Wait" very funny. a) you do not know about the living situation. Maybe it is 2 rooms at mom's attic. b) the number of properties will not increase at first, rather less. I would only do it under the condition that it fits 100%, so no compromises with the house are to be made. If I start to hesitate even for 2 minutes, I would drop it.