After submitting our application to the district, we received online access to the portal of our building authority. There we could check every day and also saw the deadlines of the respective involved "sub-authorities" that ultimately had to approve the application. The exact times/deadlines each authority/city had to complete the process were also listed there. I found that very interesting. After about 4 months (it was the peak of Corona), all areas were green and the building permit was granted. Then you only have to pay the notice from the building authority and voilà, the construction company had the important construction site sign. :)