My entire garden is in raised containers. I've been gardening like this for years. I prefer not having to get down low to work but also my plot was set on concrete so there wasn't much choice.
I started no dig only very recently by doing my best not to disturb the soil underneath and dropping fresh soil treatments at the top only. A few handfuls of compost or gardening soil is all you need, poke a hole with your finger and drop in a seedling or seed. Sprinkle some compost over top, gently pat and water. Mother nature takes care of the rest.
My favorite part about no dig is how easy the end of season is. Previously I would dig up all the old roots and till the soil for next season. This was so labour intensive I dreaded it! But now I love end of season. I simply twist out larger plants and cut smaller plants at the base making sure to leave the soil undisturbed. Then I cut the plants in small pieces and put them directly into my compost pile along with the dried fallen leaves, a few handfuls of compost and some splashes of water. Voilà - pots are ready for next spring and compost is started. Best method ever!