You can go to a bar and get a drink starting at 7am on Saturday and 10am on Sunday, and there are some bars open until 4 (or even 5) am in Chicago. Evanston might be different, but Chicago definitely will serve you before the game.
Per the
city of Chicago:
Hours of Operation
• Liquor establishments are permitted to operate between the hours of 7:00am and 2:00am Monday-Saturday and close at 3:00am on Sunday.
• Opening hours on Sunday is 10:00am for establishments with a Consumption on Premises – Incidental Activity Liquor License and 11:00am for establishments with a Packaged Goods License or Tavern license.
• Outdoor patios that serve liquor must close by 11:00pm Sunday–Thursday and at midnight on Friday and Saturday.
• A business with a Late Hour Liquor License may remain open until 4:00am Monday–Saturday and until 5:00am on Sunday.