Hi Jen,
Welcome. I started a new allotment last April and it was full of waist high nettles, thistles, dyers weld, couch grass and clover. I only used cardboard. I cut the weeds level and put cardboard on top with between 4and 6 inches of compost on top depending on what I was growing. The cardboard was free from Morrison’s. I collected their banana boxes daily and opened them up, using them double. I used them for the paths, too. I put branches on top to hold the cardboard down until it was well soaked and flat and had plenty of overlap. Some bits I pegged weed control fabric over to hold down the cardboard. Then I gradually made my beds and planted straightaway.
There is very little regrowth of the perennials. The odd nettle pokes through and the odd thistle, easy to remove. This season the cardboard has obviously composted as I can plant as deep as I want everywhere and still very few weeds are coming through. Hope this helps