No construction start date from the house building company! What can we do?

First, calmly pour your foundation slab. That is more work than you think. It took me a good 3 months until it was finished. (Ohne Bagger)

We are now unfortunately being kept waiting. Now the company claims that the production of the house will only BEGIN once the base slab of the house has been ACCEPTED.

Exactly like this and no other way. Period.

Is that legal? Can we possibly contest it?

Yes, it is legal. You signed it.
What do you want to contest?
It would have been wise to have the contract reviewed. _Before_ signing. It also often goes faster if the foundation slab is built or ordered through the house builder company.
But now it is as it is. Take care of the foundation slab and inform yourselves about further steps before something arises or is artificially delayed.
Read the contract again before other problems occur.
Unfortunately, I have the feeling that you somehow want to get out of the whole house-building thing – for whatever reason.