How expensive can the property be?

At least in Berlin, until the rent cap (and whether it will hold remains to be seen) it was different. Rents (for new leases) have also risen beyond the cap.
Now with the rent cap, the thing is that you first have to get hold of a suitable property at all, or it has to appear on the public market in the first place.

Well, I'm curious to see how it will continue.

I can agree. We live 50 km from Berlin. Our apartment costs €567 warm (70 sqm). When re-letting, the price rises to about €800.

It's more about the fact that they sometimes want to completely talk them out of the possibility of acquiring a home. 50s..60s era building for €150,000-200,000 + €100,000 renovation costs, a lot of personal effort, and off we go.

With some creativity and willpower, there is an intermediate step. Buy the plot of land and a mobile tiny house - 2 people and young - that would have suited me. Develop the plot and "dock" the tiny house to it. This way you can quickly live in your own house on your own land at manageable costs and continue to save capital. If then you feel like building a bigger house, you sell the tiny house (at a loss), but you already own the land (which will probably have increased in price by then). Financially, it should therefore remain "neutral".

New construction is not feasible at the moment, but and I agree with some on this point, you have to be creative. You are young and also civil servants, so you can stretch it. For example, ING offers a 1% repayment rate, after which you can increase it.

The factor that the start of construction might only be in 1-2 years is neglected, and you can also stretch that into the 3rd year, then the baby is 3 and the wife can work...
As of today, you won’t manage it, which is not a problem because such things are approached in the long term and that is the problem with many people, which is why we have this rental mentality in Germany and everyone wonders why citizens abroad have more wealth. Homeownership is normal there...

My suggestion to you. Finance the land, try to work with a special repayment there, and plan the construction in 2 years. Not everyone can have 5k net at least and then build.
If you change your mind, you can easily sell a plot of land in such an area...

There are also DH or ETW. Buying turnkey keeps the risk manageable and you stay within budget. I find €3,100 as a graduate in civil servant status with tax class 3 rather a low income. Sorry, you just have to lower your expectations.

it's more about the fact that they sometimes want to completely talk them out of the possibility of buying their own home. 50s..60s construction for 150,000-200,000 € + 100,000 € renovation costs, a lot of own work and off you go on the wild ride.

Could be an option, but it's not for everyone. You should be handy and have to invest a lot of time alongside a full-time job. If you also want to spend time with your small child, you can pretty much forget it. And even if you manage all of that, you either have a double burden or live on a permanent construction site. Neither is great, and in this case, neither is advisable financially nor because of the small child.
There are simply situations where building or buying a house is really difficult to realize. And even if everything went smoothly, it would still be associated with many restrictions.