I've wondered about this myself, so I'll give you the explanation and speculation I have.

Remember it's tradition for only the kings and lords to go in the crypts, so the crypts wouldn't fill up that fast. Literally one addition per generation (until Ned broke tradition). Winterfell has a lichyard for their other dead.

Iirc when Ned and Robert visit the crypts it's noted that they walk past many lords' graves to get to Lyanna's tomb, and that there are many empty spaces to fill.

It is weird that that the first kings were buried lower down, however, perhaps there were only intended to be those lower levels until they collapsed, and another floor was built above. Once that gets full (which will take hundreds of years) I imagine the Starks will keep building outward underground, so not run out of room. In thousands of years, if it hasn't happened already, the crypts may form a very long tunnel that connects to other caves (as others in this thread have speculated, perhaps to Gorne's Way).