Yep, that’s probably not the most elegant solution. If you have to build a basement anyway, because otherwise you will be ostracized, then build it underneath the garage and drive in directly from the street above. If it goes down that steeply (4m?), the entrance from the street just has to be on the upper floor. Paving over the garden with a mega-long driveway is nonsense.
Really, the project screams for an architect. It can turn out great with the architect or really terrible without one.