veggies4me, I will type all the thoughts that occur to me.

1. Set up a motion activated camera.
2. Look for and identify any and all animal tracks/pawprints.
3. Ditto for feces/excrement.
4. Live trap.
   Sorry! I was hopeful that something specific would turn up.

Chipmunks and mice would both be possibilities. A cheaper way to check that could tell you at least if its a night feeding something that moves slowly, caterpillar, cutworm, wouldn't think slugs or snails would be a big issue for you there, is to go out after dark with a flashlight and look. You may have to make more than one trip, beginning not long after dusk. Free, and it can't hurt - who knows, you may just discover your culprit and know then how to treat.

I've been amazed at what I find in my garden after dark :)

Cutworms do not eat the whole plant, grubs feed on roots and would not eat the whole plant either, and slugs cut holes in plant leaves and do not eat whole plants.
What would eat whole plants would be Rabbits, Deer, Gophers and Groundhogs, etc. Skunks, Raccoons, Opossums, etc. might.
How well fenced in is the garden?

Kimser, climbing cutworms could indeed consume entire seedlings, just as they can eat entire leathery leaves of large leafed rhododendron...

I wouldn't think lizards would go after those kinds of plants. Around where I am, squirrels steal food, but I have broccoli, and they (so far) have ignored it. It's even next to the fence where they constantly travel on.

Could it be some kind of wild cat or a dog?

It might be hard to look for prints unless you have very soft soil, like sand. Maybe put down some thin pans with a food coloring in them. They might walk in it and leave footprints, or maybe leave a trail of prints elsewhere.

Going out at dark is a good idea too. It might be time for some undercover surveillance!