Emphatically, no till!
The structure of your soil, the profile that supports your turf, the biology of the soil are all the right way up, why confuse it.
Suppress the grass,ie mow it, blind it, stop it growing by cutting off its life support (light)
Add the compost to feed the microbes that feed your (future) plants.
Plant.
Your soil will contain diverse seeds from previous seasons. Only those near the top will grow, its proportional to their size. Why would you want to bring up all those from lower levels?.Just weed ,if necessary ,the surface as your crops develop. You may need to extract a few larger emergees from the lower levels (such as docks, sprouting acorns,suchlike) initially.
Trust me-it works.
Cleansweep
