Moving to Germany on a short stay Visa

Sorry to say, there is no way to convert a 7-days tourist visa into any other visa that would allow you to stay longer. And once you overstay your 7 days illegally, you lost your chance to get a longer erm visa altogether (apart from the fact that your sponsor will then have to pay for all costs associated with finding, incarcerating and deporting you, which can easily be €10000 and more).
Please reconsider your plan. To stay in Germany longer, you m,ust apply for a long-term visa from the German embassy in your country!

Beppi  is right. What you are planning is completely illegal and not going to work.  There is no rationalizing one’s way around the rules and nobody here would help you to do so. Even if you could stay for longer and take a German course, this will not get you a work permit. If you already had legal residency in Germany then you might have the legal situation to take a job. You cannot do so on any kind of tourist visa. And no employer is going to help you get a work visa and go to Germany unless you have experience and skills they need. For unskilled labor you won’t find anyone to do this nor be eligible for a job seekers visa either. And most scenarios of immigrating to German will mean having a decent level of German already.

Possibilities; get a good education, marketable skills and learn good German and then apply for jobs online or apply for a job seekers visa. Otherwise, marry a German who has enough income and a  big enough accommodation to get you a family reunion visa but this will also mean passing a A1 level German exam. Or find a well-educated non-EU spouse that can qualify for a blue card visa and find a good job in Germany and then you could come on a family reunion visa without even having the German test.