K.C.
I have always heard you shouldn't be able to fit more than two fingers between the strap and their chest. Have you tried checking that way rather than trying to pinch?
My only other suggestion is just to make sure that you have the straps at the proper level for where their shoulders are. Rear-facing babies should have the straps coming out from below their shoulders; forward facing babies should have the straps coming from above their shoulders. If the straps aren't in the right holes, the height might make it so you can't pull them tight enough.