No till solution with raised beds that are full of tall weeds?

I’ve inherited some raised beds at a place I recently moved to. The bed framing is in good shape, but there have not been any growing happening for about 5 years, and the bed is completely full with weeds that are 5 feet tall.

Could I cut the weeds at the ground, then put cardboard down and compost on top of that and plant right into it. Or will the weeds still come up?

Is there a better way to do start my garden?