How to check that a timing belt is in sync with other engine components, e.g., that a spark happens exactly at the top dead center?
Engine: 2JZ-GE
Car: Lexus GS300 1995; automatic, 250k miles.
The engine dies immediately after the start, a video of which can be found here: https://carkiller.com/scottykilmer/postid/132568/


The spark never happens at exactly top dead center. It's always a couple of degrees before top dead center. The ignition timing is usually controlled by the cam position sensor. If your belt was that far off, you'd have pistons and valves crashing together. It sounds more like a fuel related problem, ie, injectors, fuel pressure, filter, fuel pump, etc.
There should be a small line or marking on each pulley. And they usually have to line up with another line/marking beside the pulley.
For example, my 1999 Honda Accord had a line on the pulley and a triangle arrow symbol to line it up with.
It took me hours to get it all lined up correctly (I’m not a mechanic). I could get the belt on easy, but one pulley or another would always skip a tooth, from all the giggling I did.
Make sure to check each of the pulleys at the camshaft and the crankshaft.
There may be a diagram of how all the lines/markings lineup online for your specific engine.
And yes, make sure to rotate it a few times, so you know it us in time!