The first step: The No. 6 Horned Frogs (11-1) must beat No. 9 Mississippi (9-3) in the Peach Bowl.
A victory Wednesday could serve as a springboard into next year as TCU seeks more respect after getting left out of the inaugural four-team national playoff.
The Horned Frogs, facing a Southeastern Conference opponent for the first time since losing the 2013 opener to LSU, want to prove they belong on college football's biggest stage.
''Not just for me, but looking on it next year, if we win this game we feel like we can be a top team next year and compete for a national championship,'' Boykin said Monday. ''That's our ultimate goal: to try to win a national championship.''
Boykin, the Big 12 offensive player of the year, plans to return as a senior next season after finishing fourth in the Heisman Trophy voting.
He leads an offense that ranks No. 2 nationally in scoring and fourth in total yards. At least statistically, the Frogs match up well against an Ole Miss defense that ranks No. 1 in scoring and 12th in total yards.
Rebels defensive coordinator Dave Wommack has been impressed with Boykin's improvement this year in the pocket. Boykin has become more than just a mobile quarterback now that he's learned to read coverages correctly and sidestep pressure and blitzes under first-year co-offensive coordinators Doug Meacham and Sonny Cumbie.
''They work a tremendous amount on feet, vision, reads, anticipation, accuracy - all those things,'' Wommack said. ''He's just done a good job of not just being an athletic guy running around. He's developed into a pocket quarterback as well.''
Boykin wants the offense to stay calm if Ole Miss' pass rush has success early in the game. Patience is a big part of the changes TCU's offense made under Meacham and Cumbie.
''We knew that they could help us and we basically all bought in,'' Boykin said. ''It was a long spring and summer, but to be here at this bowl game has paid off. This is our reward.''
Ole Miss is coming off a 31-17 victory over then-No. 4 Mississippi State that stopped a three-game SEC losing streak.
Senquez Golson, an All-America cornerback who's second in the nation with nine interceptions, believes the Rebels must be prepared to extend coverages so Boykin will have fewer options with his top two receivers, Josh Doctson and Kolby Listenbee.
''Going into the game with a good quarterback, there's always a red flag,'' Golson said. ''As a cornerback group, we know we're going to have to cover longer.''
Ole Miss free safety Cody Prewitt says he understands how the Frogs might feel slighted on a national scale. Prewitt, a first-team All-SEC selection, is a senior who spent his first three seasons watching Alabama, Auburn, LSU and Texas A&M get most of the attention in the league's powerful West division.
''The media, people and blogs talk about the SEC being one of the more dominant conferences in the nation, I guess,'' Prewitt said. ''And that always comes with the teams that we play out of conference. They have a chip on their back and rightfully so.''
Even so, the Rebels still want to represent the SEC well.
''We understand the magnitude of how we play football in the SEC and how everybody perceives the SEC throughout the country,'' defensive end C.J. Johnson said, ''so it's really big for us to represent the SEC on this stage.''
And it's important for the Frogs to give a good showing against the nation's most powerful conference, particularly in the city that annually hosts the SEC championship game and is new home to the College Football Hall of Fame.
''I'm loving the atmosphere,'' TCU center Joey Hunt said. ''The SEC atmosphere is bigger than the Big 12. It is what it is, but I don't think anybody is scared. We're just ready to play in the SEC country.''