"The...60's?" Jim is currently very confused, confused more by the man's insistence that he knows him, that he thinks of Jim as some sort of...someone else, without actually knowing. "We're still a few years off of that." Assuming the man means the 2260's, which he probably does. It's the most logical option.

"I explore the galaxy on a mission of peace in a starship, yes." Jim frowns. "Well, not at the moment, obviously."