The alpha phase will start at the end of this month, and Xbox One players will be able to get into game on the 30th of October, 24 hours before both PlayStation 4 players and PC players.
Players who own a pre-order of Evolve will be given instant access to the big alpha phase on either October 30th or October 31st depending on the platform that player owns, however there will be chances for those that have signed up to the alpha to get access to it regardless of whether they purchased the game or not.
It would make sense that the amount of alpha slots for those who have not pre-ordered is limited, however we do not know how limited the slots will be at this time.
Once the alpha phase for Evolve starts, it will continue over the Halloween weekend and into November, before ending on the 2nd of next month.
If Evolve has taken your interest since it's announcement, I would certainly suggest giving it a try at the end of the month, as I'm sure the alpha stage will give you a good idea of what the game will be like. I personally can not wait to see how Evolve will play out.