My Einbürgerungstest is still 1.5 months away. Is it a good idea to start the application now?

I live in Mainz and as far as I understand, to kickstart the application process I have to send an email to them containing the result of the Quick-Check.

I read many posts here that saying they only get respond back to submit the documents months later. So I am thinking to just send the email now to get earlier start. Anyone have done the same?