No, sandboxes can’t have structure/plot/timeline. The definition of a sandbox is a place for unstructured play, where maybe the setting is defined. You know, like an actual sandbox. Where little kids do whatever, in the same place but not really cooperating on the same thing.

If it has a continuous and consistent narrative, rules, mechanics, npcs, then it’s a game. One you’re not welcome in, but you’re not welcome at some random stranger’s living room D&D game either.