If it's like the piano hinge i've used, you can't use bolts or nuts because they'd get in the way of the hinge closing.
If you don't think the screws are long enough just go buy some that are tad longer, but the same size otherwise. No need to countersink anything, though you might want to cut a VERY shallow dado on the cab and the door so the hinge fits nice and flush, otherwise, you'll have a pretty sizable gap.
If it's 30x30, that seems like a big door. I believe those screw holes are about 4" apart, so that's about 7 screws into both the cab and the door. I'd think that'd be enough to hold, but MDF is pretty easy to pull out of so longer screws wouldn't hurt.
Plus you probably want to drill pilot holes, to make sure you don't blow out the sides of the MDF when screwing the screws in.