How can I vent my kitchen exhaust through vinyl soffit?
Chances are good that there was still enough airflow happening with the vented soffit panel in place. I'd try it out with the new fan and see how well it works before cutting the soffit up.

Since the vinyl soffit was applied directly over the plywood soffit, you could install J-channel around the vent and cut the soffit to fit. 

You could also replace the solid panel covering part of the vent with a vented panel.