I'm pretty sure the last thing the internet needs is someone explaining the Very Precious process they used to create an NCAA bracket for their small children, but filling non-existent internet holes is sort of a thing I do, so here we go.
Process for self: Spend 45 seconds picking the name you like best, with some (little) weight given to seeding. Don't advance the home team very far, it's your husband's known weak spot and your only chance at an advantage.
Process for the 2.5-year-old: read every matchup out loud and let her pick a name. Be amused when she solidly supports Georgetown for the win.
Process for the infant: decide it would be cute to base it on how cuddly the mascot is. Spend the rest of your afternoon buried in research, and the following questions: Is it what the mascot would be like in real life, or just the costume? (A grizzly bear is not very huggy, but a giant bear costume is.) When a mascot is abstract but has a cute animal representation, what do you do? (Looking at you, Alabama.) Should you immediately disqualify creepy humanoid mascots? (Yes.) And birds? (Yes.) Killer cat or killer dog? (Depends on their demeanor.) What if two creepy humanoids are head to head? (Think about it for ten minutes, pick one and move on.)
And there you have it! Several hours of surprisingly hard work so that you and your daughters can all lose to your husband, who probably spent 10 minutes looking at sports news.