Trying to aerate clay soil, but can’t get very deep

Is my aeration pointless if I can only get this deep in the soil? Like an inch or so wherever I go.

It’s clay soil, and I am trying to renovate the whole lawn with aeration, fresh top soil, compost, and manure before overseeding.

I am pulling out soil cores, but only small ones each time.

I’ve tried softening the soil ahead of doing this by watering it heavily with the hose yesterday and a couple of hours before this attempt this morning