Welcome to the forum Sarah Jane.
Yes you can sow and plant into a compost or manure mulch, just as long as it is broken down enough to draw out a drill. If we get some frost the surface lumps will break up more, just as lumps of dug soil do. You can knock them around with a rake to make a better tilth.
I sow carrots, parsnips, spinach, leeks and radish into the surface mulch of compost or manure in spring. Other vegetables are raised undercover and planted out, and potatoes go in a hole made with a trowel, then have some extra organic matter on top to ‘earth them up’.
Perhaps the hardest thing with no dig is trusting nature to take care of things, especially if you have been used to working hard with soil to ‘knock it into shape’. I have a few failures every year, as do all gardeners, but on the whole growth is wonderful and weeds are less once the soil settles down.
So enjoy the journey.