Most gun safes these days have a built in lock, and whether or not that can be made smart depends entirely on the brand and model of the gun safe. Some can, but most can’t.
if it doesn’t have a built-in lock, then It would be the same as making any cabinet smart. You just add a lock that smartthings can control and then add Alexa to it. ( i’m not saying this is a good idea, I’m just saying that you can. 
) there are several existing forum threads on making cabinets smart. Here’s a recent one:
Smart Drawer Locks - Help Needed!
All of that said, though, it should be noted that some homeowners associations, some townships, some insurance policies, and some specific court orders including custody agreements may have details about gunsafes with regard to keeping children safe, and I’m not sure that any Alexa-operated method would meet those requirements. So that’s just something you would have to look into.