We have a some stuff like this in our barn. I'm going to go into the "leave it" camp.
You can push it back out a bit but it won't be perfect short of a professional restoration and to me, that looks worse than the dent. Plus, on some antique things I like the character of a well used item.
If I just had to make an attempt, I'd lay that front side down on a flat wooden work bench and use a rubber mallet with some mid sized blows to push the dent back out a little. I would NOT attempt to remove it completely because you won't get the crease out and it will look like a half hearted attempt.
Houston-BCS-Austin-Dallas-San Antonio - Infinity Roofing - https://linqapp.com/jason_duke --- JasonDuke@InfinityRoofer.com --- https://infinityrooferjason.blogspot.com/