Hmmm, a backfire out the carb or exhaust is 99% timing. other than that its engine damage that you dont have. You probably did this a few times but recheck the timing. also check that the cam is timed right. number 1 piston up on compression stroke (use you finger or a gauge to see when your on the compression stroke )with damper on TDC ( pointer is correct, right )
and dist rotor at cap tower you want #1 to be at or at stock location. If it back fires out the carb your intakes are open and you should move the dist clockwise 1 post and if it backfires out the exhaust move is back 1 post, this only if you cant move the dist enough to get it started or it hits the water neck.
As for a later 5.0 cam installed, yes this can happen. I run a 5.0 cam in my 65 stang 347. You have alot more choices and the pro's say the firing order produces more power. The firing order is 1,3,7,2,6,5,4,8.
You can check for this cam by checking the first 3 cylinders that fire on the compression stroke. This will tell you what cam you have, old style or 5.0 style.
Good luck.