Hello, and welcome to the Forum.
Just clip or mow the weeds (and compost them) and then till and amend the whole bed. Amend with a nutrient-rich organic matter. Compost is ideal, but various manures and bagged or bulk amendment blends will work fine. Even if you are attempting a no-till/low-till vegetable garden, still do initial tilling and amending to prepare the bed for its new role. After planting or seedling emergence, do mulch the bed with additional organic matter. Hoe or hand weed as necessary.