From the way sewing machines work, I would expect that the timing belt is in the column. See of there is a cover that you can open.
You can also remove the plates around the needle foot to see what's happening below. If the foot is removable, take that off too.
basic idea.
https://www.youtube.com/watch?v=lT98wbDLVco shows a real machine and explains where the hook should be relative to the needle path.
Normally the action will work something like this:
Needle comes down, and punches through the fabric,
Needle starts up. Depending on the cams internally, it may pause briefly. As it comes up a bow is formed on the tail thread. (one furthest from the spool)
The bobbin hook catches this thread and caries it around about 2/3 of a circle.. The tensioning lever rises and pulls up the extra slack.
Next thing: Try a search on youtube for your make and model of sewing machine.