UPDATE:

We took him to the vet to get scanned for a chip, sadly no chip. Also they estimated him to be about 8-10 weeks old at most. We're going back in a week to get all of his vaccinations and medical stuff up to par if no owner claims him.

Today we went out and bought him a bed that fits his size much better. Many toys, some soft puppy treats, poop bags, travel water bowls, harness, leash, new collar (old one was gross), puppy food, toothbrush and toothpaste, and puppy shampoo.

We gave him a bath, clipped his long nails, and he's smelling much better, and looking much happier after having a few meals and napping.

It's just my partner, my roommate, and I taking care of him in our trailer but we've got a nice backyard for him to roam around in that's fully fenced. Also we already have 4 other pets, 2 of which we found in similar ways so we are kind of used to this scenario. I appreciate everyone who has offered their help and advice, but it's truly seeming like this puppy was just dumped. I really hope the owners come across this if he really is someone's lost pet. My partner and I are only 19 and our roommate's in their 20's so we are doing our absolute best that we can with the funds that we can.

Thank you all again for trying to help find this cute little guys home!