For this situation to work out, the person who finds the baby has to be someone who wants a kid in the first place and who wants to adopt (or would consider adoption instead of biologically producing). I don't want kids at all, so I wouldn't adopt one just because I found one abandoned. The kid deserves a parent who is ready, willing, and able to be a parent. Clearly, at least one of the biological parents did not fit that description.

If you do want a kid and one drops into your lap like this, attempts still have to be made (preferably by law enforcement) to find the original parents and figure out what happened. What if one of them kidnapped and dumped the baby, and the other one is a perfectly fit parent? Or what if there was a third-party kidnapper? A lost baby isn't necessarily an unwanted or abandoned one.

If it turns out that giving the kid back to them is not an option, whatever child services exist in the area will try to find adoptive parents. You wouldn't get bumped to the front of that line just because you were the one who found or rescued the kid -- you'd have to go through the same application and screening process as any other prospective parents, and chances are there's a long waiting list ahead of you.