At some point, the Mandalorian is going to have to pass the Asset off to someone that can take better care of him. Who will that be? The possibilities are exciting. This show takes place about 5 years after the events of Return of the Jedi.
The Asset is force sensitive, so it makes the most since for him to eventually turn him over to someone with the force.
Remember one of the main creative individuals behind this show is Dave Filoni of both The Clone Wars and Rebels. Could he possibly pass the little guy over to Ahsoka Tano? That would be amazing. We left off the end of Rebels which takes place right before the events of A New Hope with Ahsoka heading off with Sabine (A Mandalorian) in search of Ezra. Die-hard Star Wars fans would go nuts if Ahsoka showed up in live-action I could totally see that happening.
My second thought comes from recently watching Captain Marvel on Disney+. Marvel did such an amazing job with a de-aged Samuel L Jackson that the show could easily end with The Mandalorian handing Baby Yoda over to Luke Skywalker played be a De-Aged Mark Hamill. Season 1 could end with him giving the child over to Luke Skywalker and then Season 2 could start with Luke tossing Baby Yoda over his shoulder (Just kidding).