I think every gardener can appreciate your situation. If you have seeded veggies in rows, I have found the best way is to get down on the knees on a garden pad and pull them by hand. I can quickly pull the weeds in between the rows and then I focus on the weeds closer to the veggie seedlings. I pull them carefully, one at a time, around the vegetable seedlings. I then hill some soil around the disturbed veggie seedlings and carefully water as soon as possible to minimize plant stress. I think the number one trick is to pull weeds when they are small - they are easier to pull and have smaller root systems so the veggie seedlings are disturbed as little as possible. Once the area is weeded, maintain it by pulling some of the new weeds every time you go to the garden.
If the weeds near the veggie seedlings are too big to safely pull, then cut them off with a pruning shears and continue to remove any new growth until your veggies are harvested.

I do not do block planting so I have no advice to offer you if this is your seeding method other than to remove the weeds when they are young.

Whatever happens, do not give up on gardening. Weeds are very frustrating but you will be better off stress-wise by accepting that this problem will occur every season. Weeds must be dealt with to get a good harvest so experiment and find what works best in your situation. Many, many weed control methods and strategies exist out there and are used with varying degrees of success.