Basically, a flat surface is to be created.
Where? How much? A slope remains a slope. Excavating or filling is usually more expensive than one thinks. The resulting walls need retaining walls, and rainwater disposal often costs extra. To achieve an effect with 2 terraces (south and north), these are galactic masses. With a total budget of 650K including 3 children's rooms, an office, and all that, in my opinion, it's unthinkable. Moreover, my focus would certainly not be the direct connection of the garage to the house, but rather cost minimization in terrain modeling and the necessary rooms in the house. I would recommend choosing one terrace, either south or north, and orienting the house accordingly. The north terrace offers the advantage of short distances (every sqm costs), shading in summer (exactly when you like to be outside), and shielding from the street by the house. After that, one can look at where the garage can be placed.