My bet is rabbits

Squirrels ate ours. The chard kept trying to grow, then the gray devils would come back for more.

We don't have rabbits or deer...

Slugs, snails and earwigs are more likely culprits to eat and destroy tiny sprouts. I rate slugs number one suspect.

Slugs for sure. Every see them clean up a row of newly sprouted carrots?

If it is slugs and weather is not too hot and number of plants you have is reasonable, you can use local protection.
What you need:
1) 2 litters clear plastic bottles(I use bottles from sparkling water ), one per plant or one per two plants depending on how high you want to grow them undercover.
2) Tulle fabric
3) Large rubber bands

Cut the bottom and top from the bottle. You may also cut it in half to make two cylinders instead of one.
Cut a piece of tulle enough to cover one end of the cylinder
Fix it on the cylinder with rubber band. If you do not have rubber bands you may punch the holes on the edge of the cylinder and sew the tulle to it, or even use hot glue to glue it.
Now seed several seeds in the circle that is less that cylinder and install cylinder on top of them, pushing it well in the soil. When seeds germinate, lift cylinder, thin and install cylinder back.
Unfortunately, I came up with this idea too late - my cabbage seedling already been damaged. And I only had 2 bottles ready to make 4 cylinders. Those I covered - recovering... The rest - most likely will not survive. Slugs dinner out every day)

Do not cover your plants in the very hot weather - it will be even hotter in the cylinder despite opening on top. You can take it off during the day and install back in the evening.

I like the bottle idea! I have been thinking of some kind of enclosure - thank you for the design idea!

I have never seen a slug (it is very dry around the bed, xerisaped basically) but have seen many earwigs and brown caterpillars.... We don't have rabbits or deer but do have squirrels though this seems too tiny/focused damage for a squirrel.

Will this help with those pests or do they burrow deep enough underneath?

could be cutworms...they come out at night from soil....

I don't think bottle will help with squirrels - they will knock it out. With the rest of the bugs, as soon as they do not come from soil - it should help.