An initial digging and even double digging may be needed for this purpose. Compost is incorporate without stint, so as to ensure that you will not need to repeat the chore. It is, if you like, a kind of super topsoil, replacing the annual leaf-fall of the forest. As such, it should be placed where the leaves fall - on the surface.
Ensuring a Frost Tilth
This is an even less valid argument for digging. Creating a tilth becomes necessary only because the soil has been dug and made lumpy. Healthy, well composted soil has a pleasant tilth all the time - even clay, if it is well managed. Following a frosty winter, this is especially the case, if the soil has been spared a digging.