If it’s spinning as if there’s no compression and then try to start like there is compression, the starter’s gear may not be properly engaging with the flywheel’s ring gear to turn the crankshaft. That’s a starter-assembly internal problem. You can’t tell anything just by looking at it unless you know what to look for.
The other possibility is that the flywheel ring gear is missing some teeth… and the starter motor gear is occasionally hitting the spaces where the teeth used to be, spinning freely before catching a tooth. Honestly, since the starter motor circuit seems to be enabling properly, this would be my guess. It suggests that the Bendix assembly that engages the gears AND closes contacts that enable the starter motor is functioning. A knowledgeable mechanic will have to inspect the flywheel ring gear as a colleague slowly turns the crankshaft.
fyi, I’ve experienced something like this w/my truck when it had a problem where it was leaking fuel into the intake manifold, causing it to flood out. When this happened, it sounded like it had low compression during cranking, then eventually it would pop and run ok, with full power. I think the compression was always fine, but something about the intake manifold being saturated with gas made it sound or at least seem like it had low compression. After I fixed the flooding problem, now it sounds like it always has during cranking.
I pulled the covers off the timing belt cover and discovered the belt is intact. However, there is a lot of fiber debry from where the outside edge of the belt appears to be wearing out. I think the belt may have jumped time, but I am unsure at this point. I need to find my socket and tool to remove the crankshaft to check the timing to be sure.
On my Corolla anyway as long as you can see the camshaft pulley(s), no need to do anything with the crankshaft to verify the valve timing. Just place the crankshaft at TDC. The camshaft alignment marks should then also line up. If not, rotate the engine 360 degrees and check again. You might be at TDC on the exhaust stroke. The crankshaft has to be at TDC on the compression stroke for the camshaft marks to align correctly.
If that’s what you got to do, I guess you have to do it. When you reinstall the crank pulley make a mark on it where TDC is, then next time this extra job won’t be necessary. fyi, it’s often a pretty big job to remove the crank pulley. If you haven’t done it before, suggest you ask here for some pointers before attempting this the first time.
I have replaced the timing belt on 3 other cars I have owned in the past. This is the easiest one I have done thus far. It has only required 3 sockets (4 if you count the one for the crank pulley).
Your Solara has a V6 oriented with the long axis of the vehicle then? The timing belt job on that configuration seems to be a little easier to do compared to the transverse mounted I4 configuration, from the comments we get here. Not so much engine and transmission mount involvement I guess.