Estimate construction costs for a single-family house

My wife and I would like to buy a single-family house. Currently, we have a plot (from the municipality) on offer with 520 sqm for 140,000 euros (area Lahr Schwarzwald). We can spend a total of about 570,000 euros (house ready to move in including kitchen and all additional costs).

The house should have about 150 sqm and be fully basemented. The plot is on a slope; one may possibly have to reckon with hillside pressure water and build a retaining wall (about 15,000 euros).

- 2 full floors
- Rooms: bedroom, 2 children's rooms, large study, living room and large kitchen with dining area. - Terrace
- 2 parking spaces (carport or garage is not necessary)
- We probably want a controlled residential ventilation system (because of air quality)
- Proper sound insulation (also inside) and summer thermal protection are important to us

Construction method: solid (brick or cross-laminated timber).

Is the project realistic with this budget?

Feels tight, but not impossible.

Thanks for the assessment. By the way, I obviously meant "build" and not "buy" in the first sentence. The house doesn't need to be a passive house, but in terms of insulation, it only needs to be as good as legally required.

Regarding the budget, I should also mention that on the one hand we still have about 30,000 euros additionally available, but on the other hand we still need quite a lot of furniture for the new house from that money and also want to have a little something set aside in case there are unexpected construction costs. Does anyone perhaps have examples of houses in a similar category to our planned one and know what they cost?

As for the house, it should be said that there will probably be a flat roof, or possibly a shed roof, since that is the only way to make sensible use of the maximum height that the building envelope allows.

Online, you often read about what a house costs per square meter. If I now calculate backwards for our case, I come to (570000 - 15000 - 50000 -150000)/150 = 2366.7 euros per square meter of living space. In doing so, I subtracted the 15000 euros for the retaining wall and an assumed 50000 euros for the basement as well as the land from the total budget. Sometimes you read that you can get by with 2000 euros per square meter. However, it is never really explained what is included in these square meter prices. I would be very grateful for further help in estimating whether our project is realistic, as we should decide quite quickly whether to buy the land or not (there really were no alternatives within the last year; we have been looking for that long).

You have ZERO incidental construction costs in your invoice.