Extending an already extended closet into a garage

Hello all,

The master in our house came with a 5 ft wide by 2 ft deep closet that was built into the garage, having a master with a closet must have been an afterthought (along with a lot of things...). I want to extend it another 4 or so feet into the garage as my wife is pregnant and the room we were using as a dressing room is going to be the nursery.

Right now the closet is floating into the garage. The house is a wide ranch and the floor level is approx 2 feet above the garage (grade) floor. I assume they just extended joists out and framed it. The basement does not extend into the garage but the room side I cannot see where they attached the joists or whatever is supporting the floor. Right now its just floating in the garage, I assume they must have anchored it to the adjoining outer wall.

I'm sure I'm going to find some nutty stuff when I open it, my question is, what is the best way to secure it to the garage floor? I was thinking cinder-blocks and concrete fill. That's a simple L but how would I attach it to the garage floor, I was thinking drilling down the block voids into the floor and putting some rebar in before I filled the block.

I don't want to do posts, being the garage I'd feel safer knowing the support was solid and not something that could be "kicked" out or tapped by a car.

Any suggestions would be great. Thanks in advance.