if your backfiring from the intake then i would look into a timing issue.
Timing chain too loose. The sensor inside the distributor(pick up) is worn out and it is giving the computer the wrong info on firing the plugs.
You can have a stuck valve on the intake side or a valve not seating.
backfiring from the exhaust.
rich or lean misfire
timing issue, electrical and mechanical
air pump issue
electrical failure aka misfire
exhaust leak
i doubt it's you running it without a cat
first you need to figure out if its an intake or exhaust backfire, makes a huge difference.
get a vacuum gauage and see if the needle is steady. If it isn't then you may have a mechanical issue.