If you add three inches of manure, it will change the soil level by
approximately half an inch after earthworms incorporate it into the
soil.
The other posters gave good advice, but one other thing you can do if
you want to break the soil further in is to plant fava beans for the
season (after having spread the compost). If they cannot break it, no
plant can. There are other plants, all with strong taproots, that will
do the same.