you shouldn't mulch onions as you would garlic since onions will have a hard time emerging through the mulch. however after the onions emerge there should be no problem with mulching them. i never have used cardboard so i don't know about that. i use straw. i guess if you use cardboard as one would use plastic mulch then there is nothing blocking the emergence of the plant.

I always mulch mine after transplant. Mulch is more about moisture retention than weed prevention for me though.

Can l use sowdust

I always mulch onions after the leaves get maybe three inches long since weeding is a PITA, using whatever mulch can be turned in later. Grass clippings,shredded leaves, straw shorts,etc. Suppose sawdust could be used, but I never want that much carbon in the soil.

Nanyuki I would not mulch with new sawdust as it will take nitrogen from the soil that your onions need.Old rotten saw dust would be O K. Good gardening to ya YOPPER