At least, not for the time being.
P5 status comes from having a NY6 autobid. The CFP awards an autobid to the highest rated G5 champion.
Thus all you really have to do is get the best G5 teams in the same conference and start hogging the autobid, instead of watering the best teams down between the AAC and MWC.
Obviously you wouldn’t overcome the financial gap, but you would overcome the access gap and over time public perception would separate you from the rest of the G5.