Ma Nature does not like her soil left bare and exposed to the ravages of the sun, wind, and rain so she sends wild flower seeds (we often refer to them as "weeds") to grow up and cover any bare soil, so yes if you leave that soil bare those annual "weeds" will grow there.

Is that wet soil due to a lot of rain or poor drainage, or a bit of both?

kimmq is kimmsr

NJ. We went through some dry conditions now when we get rain it's a heavy soak then again a few days later. I am having the same issue in raised beds where weeds weren't an issue last year

If you pull them before seeds are dropped, you should see exponentially fewer next year. The first year of a garden spot, there's usually a disheartening explosion of unwanted plants. If you're diligent this year, next year should seem like a breeze!

You may be able to scrape the soil surface (like with the flat backside of a metal rake or flat-edge shovel) to get rid of some kinds of seedlings, then a week or 2 later, pull the tenacious ones that kept going. If you lose control in some spots, a string trimmer can chop everything off near soil level if you see flowers, to buy more time and prevent the flowers from ripening/dropping seeds for another crop of unwanted plants next year.

Between rows/plants, you can use grass from mower bag (if mowing before grass makes seeds,) straw, leaves, mulch, cardboard, pine needles, whatever organic matter you have handy, to help with weed suppression (while helping to improve the soil at the same time.)

Here are some photos.

I do not worry about the pepper plants I have since they will thrive when temp heats up. I believe one of the weeds is some morning glory type vine. Not sure about the other. All of them are small and I've hand pulled one row. The middle two rows are fulled of them. The 4th row is relatively clean, not sure why. The right row has other types of tall weeds.

I think it is easier when the weeds are like this size. It was hard to pull when they are small. I need the rain to stop, so I can pull them and add them to my compost bin. I just turned my compost bin and it is going to heat up again.

Hoe, hoe,hoe. And on a dry day.

Yes, that would do it. They do look like a nice size for pulling if you prefer, still should come up easily, and give you a decent amount of OM for composting. Or smother. Those seedlings should die easily, by any method.

The bottom pic made me think Hibiscus trionum.

I'd check at this point to make sure you're just dealing with seedlings, not growth from perennial roots (a concern when there's an unknown vine-type plant that resembles morning glory.