There are a few "easy" options that should help fix this problem.

1)Let them sprout, then fertilize, wait a couple days, and spray with round-up. Continue to water until they grow themselves to death. Then no weed seeds and the weeds are dead

2)Build your raised bed. Cover thoroughly with cardboard (will break down after the weeds are dead and not be annoying when cultivating in the future) and then soil. Careful not to puncture cardboard in your first year.

3) A firebomb type attack in which you use #1, then put down preen or casoron, then follow through with #2. This is likely to be overkill, but also likely to be the most effective method. You may have poor success with things growing for a few years in this bed as a result, but you're also unlikely to have 4-o'clocks growing in this bed either, which is the intended goal.

Did a little more reading. Looks like you may have multiple round-up applications as more and more seeds begin to germinate.

Another option would be to cover them thoroughly with black plastic sheeting and let them cook when we eventually get a few warm days this summer.