It very well could be a belt. Timing chains rarely jump except on the old American cars with Morse chains. Most engines nowdays with chains have double roller chains.
Anyway, with the manual, you should see if there is a timing diagram of some sort. You should be able to turn the crankshaft to a mark and then look at the cam mark to see if it is aligned. It might take two turns of the crankshaft to align the cam.
Checking compression is another way to check cam timing in that if the cam timing is off, so will the compression.