Some plants cannot stand to be mowed so that may get rid of many. Where it doesn't, herbicide as GG has recommended.

Most plants have trouble with the idea of being only 3 or 4 inches tall. The few who can handle it become notorious lawn weeds. The many who can't end up dead.

Thanks to all! Now I REALLY can’t wait for the first mow (but I will)

Yeah, you should be fine, my first reaction was that your new bed actually looks really great already!

First mow will get rid of some. Summer will knock out a lot of the rest combined with mowing. Anytime from 4th mow in early to midsummer in moderate weather even out to fall is time enough to use some herbicide to get rid of the remainder because, by that time, there won't be all that many anyway.

When I re-seeded, I had a gorgeous stand of celosia from where I ground up last year's garden. Or, everywhere. Even starting to blossom. They didn't survive first mow, but they were kind of funny.

Morpheus, thanks for your input and personal experience!

As a follow up, I overseeded the entire lawn (not just bed area) while I was at it. I know overseeding is best done in fall but the lawn is surrounded by tall trees and wanted to give it a shot while I had the compost and seed. The new seedlings are about 1-2 inches tall right now and the pre-existing grass is 3-4 inches. My plan is to give the yard it's first mow when the seedlings are 3-4 inches (the mature grass might be 5-6 inches high by then).

Is it ok to let the existing grass that high or would you suggest mowing a bit earlier? Also, I usually mulch my grass with mower but should I bag on first cut since the clippings will be so substantial?

Thanks again!

Bag the clippings if it looks like they'll do any smothering. It will not hurt anything to mow early, setting the mower on high/4".