Same as your other question: You may be able to set start TCs for footage in the footage interpretation and for compositions in the comp settings, respectively. Otherwise there's no way to sollve this elegantly. Unlike Premiere, Avid or others AE does not support complex rolling edits and such.
After Effects is not a video editing app (NLE). Most comps should only be a single shot or a short sequence that cannot be put together in your NLE.
If you are talking about lining up layers so they are all in sync starting at a specific timecode, then you have to do that manually in the footage or layer panel. The footage panel will show the timecode of the footage if preferences are properly set.
If this is a multi-camera shoot then by far the easiest way to set up your comp is to use Premiere Pro's Multi-Camera workspace, stack up the shots, set the new in and out points for all layers by making a cut, then just copy and paste the layers from Premiere Pro into After Effects. That takes just a few seconds. You could also just use Dynamic Link in Premiere Pro.