It looks like one of the earliest Twenties I've seen. The edge binding is typical of higher-end Cavanagh and Dobbs Homburgs from the '30s into the '50s. For a Dobbs, the frayed edge is more typical in an older hat.
What does the tag say that's sticking out from under the sweatband? I can't read it in the photo, and it's probably a big clue as to age, as it looks like a Trusize tag or an OPA or OPS tag.