2022 - Good Morning, Afternoon, Night

Trying to make more beds this afternoon, but I have completely exhausted my cardboard stash. I have used everything, down to tiny boxes like paracetamol.

I am not going to be able to get hold of large quantities of cardboard, so now what? Do I just pile the compost straight into the grass and hope for the best? I think it may be my only option as I have so many plants that are overdue being planted out. Have a horrible feeling it will just be creating a weedy rod for my own back in future, but my only other option is to put down plastic sheets (old compost bags) and then the compost and then redo it all at a later date - not appealing!!

If I'm putting compost straight down, should I dig and at least turn the turf upside down first?