The deck is incredibly thin and a regular self tapping screw won't have many threads. I believe boats of that era had wood backing blocks and chances are high, if the hardware is gone, the backing block has fallen away. Inspection ports are one option many do here. There are other methods as well, but that seems to be the most common. ....such as I cut thru the bottom of my 69 Sunfish, and epoxied aluminum plates for backers and drilled holes, tapped, and then used machine screws. I wasn't a fan of cutting on the deck, but I seem to be in the minority.
Just purchased A 1976 Sunfish from the original owner and it came with a Trailex Trailer for $300. No cubby hole in back and wooden coaming. Boat is in fantastic shape. Heck I thought the trailer was worth more than the entire purchase price. Even has little hook for main sheet..all original...
When that didn't pan out I cut a postcard-sized hole in the side and BOLTED the handle (as in above link), then epoxied the removed piece back in. Even then, there's not much space in there to fit a wrench.
When I need to replace the bridle backing plates, I'll probably use postcard-sized sections of a common $1 polypropylene cutting board.
Since there's no rear inspection port in any of my five Sunfish, I'll cut through the bottom--and repair as above.
My opinion is that repairs to the bottom will strengthen the hull in areas that flex A LOT.
What hardware is missing? And if part of the internal wooden backer block remains, yes you can fill and drill. We need more info to help figure out if block remnants are there or if the have disintegrated and/or fallen off into the hull.