It takes spark, fuel pressure, injector pulse, and compression to get an engine to run.
If the timing gear sheds a few teeth, then the valves and pistons will not be in synch to make compression. Checking it with a compression gauge will usually come up with a low number in that case. Often it will try to fire and pop back thru the intake as well as the exhaust.
Usually, if you have some lay on the floor and turn the crankshaft with a socket after you have removed the cam sensor cap, you can watch the wheel in the cam turn. It should turn steadily as the crank is turned. If, periodically, it hesitates in its rotation, and then starts again, this is a sign of missing teeth. this may be harder to spot if you are spinning it over on the starter.
When an engine has jumped time, it usually sounds a bit different while being cranked over as compared to the normal sound. You can also pull the number one plug and if it makes a very soft puff of air as it is being cranked, then you can probably assume it is not making much compression.\
If it is the timing gear, then you will need to pull the pan off and clean any debris off the oil pump pick up as well as out of the pan, etc.
Hard to believe someone would rebuild an engine and not use a new timing set
