The desire for homeownership seems to me to be excessive. Apparently, you would sacrifice a lot for it. What about your wife? Does she see it the same way?
The time for searching for land and planning is a good trial period. Usually, it lasts about 2 years or even more. During this time, you can let your equity grow significantly. It’s best to start today.
Building for 5 people is no small matter. But nowhere in the law does it say that 2 children cannot grow up in one room. You could also let all 3 sleep together and use the other room as a playroom or similar. You could also simply say that 2 children are enough.
With the house you like, you are already well above your 130m² and it lacks a full bedroom / children’s room. You can already see where this is heading. 150m² would be the minimum for five without a basement. Given the financial situation, I see that as nearly utopian.