Hi gembeb, thats a shame! I think there are two ways of going at this. One would be to wait for the weed killer to do its job and for that you will need the sunshine I think. Then you could just clear the weeds away. However, if you want to do no dig, you will be putting compost on anyway, probably with a cardboard base to stop the weeds coming through, so you could go ahead this way and start planting things into it.
My concern would be the weed killer and whether it has a residue that would get into your vegetables. I prefer to grow organically but you haven’t really been given a choice here!
Someone else might come along with some advice about the weed killer…