Certified GKH Gardening Expert
Your best bet would be to hand pull as much as you can and then add landscape fabric or moist newspaper topped with mulch to keep weed growth to a minimum.
However, you could also try sprinkling corn meal in the area, which has a chemical in it that acts as a pre-emergent on plant seeds preventing them from germinating. Sprinkling corn meal will not harm plants but will keep weeds from growing.
Another option (though not one I enjoy recommending) is the use of conventional weed killers, like Roundup. Here is an article that you may find helpful: https://www.gardeningknowhow.com/plant-problems/weeds/conventional-weed-killers.htm
Alternatively, you can try these less invasive organic approaches: https://www.gardeningknowhow.com/special/organic/homemade-pet-friendly-weed-killer.htm