If this is a wild cottontail baby rabbit, if it's eyes are open and it's big enough to be hopping around really well, ,it's old enough to care for itself and should be released back outside somewhere near the nest.
If it's still too young to be on it's own an there's no chance mom's still around to care for it, you need to find a wildlife rehabber and turn it over to them. It's good it's had something to eat now, but feeding it food its digestive tract is unused to, could cause major digestive problems for it, even to the point of being fatal. A baby wild rabbit needs specialized care so it can have the best chance of surviving and eventually be rereleased into the wild. Plus it's not legal to care for wildlife unless you have the proper license.
https://www.in.gov/dnr/fish-and-wildlife/wildlife-resources/orphaned-and-injured-animals/
If because of covid or whatever reason, you are given permission to continue to care for the baby rabbit, they should give you detailed instructions on it's care for eventual release. This link will also provide helpful info on raising a baby cottontail for release.
https://vetspace.2ndchance.info/eve...to-care-for-orphaned-wild-cottontail-bunnies/
If this is a feral domestic rabbit,, you can continue to care for it and keep it once it's raised if that's what you decide to do. You would know it's not a wild cottontail if it doesn't have the agouti coloring and/or if the nest was in a burrow in the ground and not on the surface. For it's care, I would suggest starting with food it's been used to eating outdoors like fresh unsprayed and treated grass, dandelions, etc, and make sure it's getting plenty of it, especially the grass. Then you can gradually start transitioning it onto dry food like grass hay and rabbit pellets, though slowly and sticking more with the grass hay at first. What's most important right now is to make sure it's eating.
If it's not then you do need to syringe feed regularly, though it would be best to get proper instruction from a knowledgeable rabbit vet on how to do this. Or at least watch some youtube videos. Force feeding a rabbit too quickly, can result in causing aspiration to occur, which will likely result in pneumonia developing, and this is often fatal. So going slow and giving the rabbit time to chew and swallow is essential.
And if the baby isn't continuing to eat well or won't swallow when being syringe fed, and/or it's developed diarrhea, you need to get it seen by a rabbit vet right away. A rabbit not eating for more than 12-24 hours is considered an emergency. True diarrhea is also an emergency.
https://rabbit.org/gastrointestinal-stasis-the-silent-killer-2/
https://rabbit.org/vet-listings/
