Is buying a house at all possible with our income?

With an income of 4600€, a 300k€ house should be doable. With 2000€ for living expenses, 1200€ mortgage payment and additional costs/reserves of 500€ (140m² x 4€ rounded), we come to expenses of 3700€. Without self-employment, that would be basically a "break-even" and everything that comes in above that can then be saved. You need to know how stable this extra income is and whether that is enough as a "buffer" for you. Actually, you should currently have quite a bit left over and still be able to set something aside? The house is surely still going to be built, right? It also depends on how "dense" the opportunities are in your area to find a suitable property within budget. Is this a "once-in-a-lifetime" opportunity? Or is it likely that you will find something suitable next year/the year after? In the second case, I would also say, save more! (With the salaries, you presumably live in a structurally weak area? Project manager 1800€ full time?)

I am amazed at how much equity many young people already have. I have also heard that you should bring 20% equity for a house purchase. At a price of 300,000, that is 60,000€, which seems almost unattainable to me as a young person who may have only studied for 5 or 6 years and just started with

Let's be honest, many people receive a good amount from their parents and grandparents at the latest by their wedding ("early inheritance") and can then start right away without having had to make major sacrifices beforehand. Some families have plenty of money, others don't. You can still tell after 74 years whether your grandparents were long-established large landowners or whether they came here as displaced persons with a suitcase of clothes from Pomerania, East Prussia, Silesia, etc...

or as expellees with a suitcase of clothes from Pomerania, East Prussia, Silesia, etc. came here...

Interestingly, this branch of the family (or rather my husband's) is the richest. However, we do not have any large landowners, otherwise it would probably be different.

Well, or you just set priorities early on towards building a house. I know it like that from my home village in the countryside. We were the first to open a building savings contract at the start of our training when we were 16. Sure, then the land comes from the family and suddenly you can build at 25.

I don't find 60k that unreachable now. You said you already have 20k for the EWNK, so 40k are still missing. With the living expenses you mentioned of 2k + an estimated 1k for rent and additional costs, about 1.6k should currently go into your savings account every month, which would mean saving for another 2 years and you would have the 60k and still be under 30 years old.

Financing requirement 300k with current income I find manageable, it shouldn't cause you sleepless nights. With a child it gets tighter, but that shouldn't stop you now either. Installment max. 1200,- and you can handle it well!

Since we completed the first building savings contract at 16 at the start of the apprenticeship.

That's exactly the point that was addressed... if you do the Abi and study, you have no income at all at 16. That then takes a few more years.