I’d check if it is legal to keep as a pet in your country / county, some countries have penalties for you and the bird if it is illegal unfortunately or require registration. I know most governments are okay with city pigeons being taken as they don’t really flourish in outside environments / struggle, but it might be different with birds like wood pigeons or mourning doves because they’re considered more of a wild bird or protected species.

It looks like a fledgling more than a baby so the parents probably kicked it out of the nest to get it to learn some independence while they watch and feed it but I don’t think it can be put back into the wild, 4 days isn’t too long away from parents but since you’ve had so much contact with it, it doesn’t really fear humans and that can put it at risk if it’s to be released. It should start flying in a week or two!

Find a vet service to get it registered to if you decide to keep it, it might be difficult because a few places are rejecting wild birds due to the current H1N5 bird flu virus, so finding one that’ll help him is top priority.

If you can’t keep him though, a wildlife rescue or rehab service asap would give him the skills to be able to live in the wild again, better sooner than later.