To say that we'll get 'much bigger' offers nearer the time of opening doesn't make much sense, as the nearer we get to our first game without a signed deal, the stronger the negotiating position gets for the potential sponsor.
This type of deal is a big investment from a potential sponsor, and their aren't too many organisations who just have 8 or 9 figure amounts of unallocated marketing budget lying around to be spent with less than 12 months notice.
Obviously every deal is different, but having played a peripheral role in a venue naming deal I'd say it's pretty likely that discussions with at least one preferred partner will be near completion by the time we get to a year from opening. The one I worked on took 2 years from serious expression of interest to signing of contracts, and then the public announcement was delayed by nearly 6 months.