Well. If you're talking fiction here, you could have him chase after her for a bit. But chances are that's too easy, because well, it's fiction, and what is good fiction if not a bit realistic?
Maybe there's a coffeeshop where they passed, and he can frequent it, or come back to that spot at the same time on the same day the next week. Or...perhaps he could post a "missed connections" bulletin and wax poetic about love at first sight.
Or maybe she turns out to be connected to him in some other way. Admittedly, these ideas are rather trite. It's fascinating to be involved in the artistic process of a novelist, though. What made you want to start?