It can be done easily with Span Crete. Span Crete is a brand of precast concrete panels, DynaCore is another. Depending on the strength needed, the panel depth changes and prestressed cable is placed in the form. There are hollows that run through the length of the panel, or you can have it insulated with foam.
The bottom of the panels are smooth, and the top will need a coating of "grout"- a pumpable cement. The panels are set in place with a crane.
Span length and load will dictate panel construction. It may be possible to eliminate any supports in the center.
Openings and steel framing for things like stairs can be engineered in.
It is very strong, many multi-story condos are built with this construction, so are parking garages. A five story condo complex I worked on had an unsupported (center) span of about 50 feet, the panels were 12 inches thick and 4 feet wide.
It should be cheaper than conventional formed in place construction.
For the square footage they occupy, cars do not weigh much. A pile of boxes filled with papers occupying the same space as a car would weigh much more. Make sure the engineer (and you) know the intended use of the space.
Consult an engineer/architect to run a cost analysis.