Buffalo Seer's gender is determined by the player. They can be male, female, or agender. That way most people can feel included :].
And, yep, getting on a certain route does have to do with a selection at the beginning. While you're still in the dark room, Seer looks into their own future. You then get to decide what Seer saw in the future by clicking on one of the three different tables shown. The future where you end up with January is the fancy table on the very right.