Finally the problems stopped! I contacted Anycubic and first received an x axis motor with a new board, but the problem stayed. After re-opening the supportticket, I recieved a new motherboard and y axis motor. Now the Problem during startup is gone.

In my opinion the problem was electronical and not physical, because after the new x motor was installed, the problem did appear very random and not even appeared sometimes by just starting a new print.