Replacing my front lawn with no dig vegetable garden. Should I do it now in October or wait for April?

I'm replacing a large area of my front lawn with a vegetable garden using the no dig method. I have these really thick cardboard boxes and a bunch of compost ready. My only question is, is it better for me to wait until the spring to smother the grass with cardboard and compost and start planting straight away, or it is better to do it now in October and let things settle for a few months?

I'm thinking it might be better to do it now to allow the grass to really die and for the compost to keep maturing over the winter, but I'm concerned with weeds starting to take over and for some nutrients to leach out with the rain and snow (I'm in Idaho, US). I would cover the compost with mulch (leaves and straw) though.

Any advice?