Obviously, it's a National Championship. Data on 1st year starters winning a NC since 1996.
1. Craig Krenzel Ohio St. '02. Redshirt Junior non-transfer. 4th year in program. Solid game manager.
2. Matt Leinart USC '03. Redshirt sophomore who won out against *Matt Cassel in camp and won title in 1st year as starter. 3rd year in program. All-world QB recruit
3. Cam Newton Auburn '10. Redshirt Junior with 2 years with one year as a backup QB in FL, playing in 5 games, followed by a medical redshirt. After getting kicked of an Urban Meyer-led Florida Team (a real accomplishment) for stealing a laptop and cheating, he played 1 year in JUCO before being **sold to the highest bidder by his father to Auburn. Highly-sought after Blue Chip and JuCo recruit.
4. Jameis Winston FSU '13. Redshirt Sophomore. Second year in program. Best Dual Threat recruit.
5. Jake Coker Bama '15. Redshirt Senior. Competed and lost vs. Winson at FSU for 2 year, transferred to Bama where he competed and lost to be starting QB for 1 year before winning the competition the following year.
7. Trevor Lawrence Clemson '18. True Freshman generational QB recruit. Didn't lose a game until the NC the following year vs. generational LSU team that was one of the most dominant offenses of all time (at least 3 potential NFL HOFers at QB/WR with Burrow, Chase, and Jefferson).
ND certainly isn't disqualified from winning a NC with first year starter. Both QBs have 2+ offseasons (both were early enrollees). Looking at the list above, the situation that is most similar if Carr wins out is Jameis Winston. Minchey has plenty of time in the program and compares to Leinart, Coker or Craig Krenzel.
It will be a difficult climb, however, especially with the front-loaded schedule. If ND can start 1-1 or 2-0 and avoid a big loss afterwards, it is more likely now than pre-playoff era that a first year starting QB gets into the groove as a lower-seed playoff team to make a run. It also helps ND has such a strong RB room. We'll see what happens.
*Matt Cassel has one of the most interesting stories in football. He was never a starting QB in college and had a pretty good pro career (Pro Bowl 2010). In fact, he WON more NFL GAMES as a starter than he had PASSES ATTEMPTED in his whole COLLEGE CAREER.
** NCAA was not able to prove Auburn paid Newton's father after Miss St. alleged the father solicited money for Cam to transfer there.