No, findings of disputed fact - like when Musk had reason to know of his injury, are determined by a jury (or a bench judge). Appeals courts examine whether the law was applied correctly, not what the jury's fact finding was. There may be an avenue of appeal that the jury was improperly instructed, but determining questions of fact are exactly -not- the bread and butter of an appeals court.
[0] Assuming that the trial judge didn't materially screw up in admitting or excluding evidence, or in instructing the jury about the law, and also assuming no proof of juror bias or improper influence.
It's a foundational issue that goes to whether the court is even allowed to proceed with the case. A defendant could be guilty/liable/whatever of the alleged claims, and it wouldn't matter. If the statute of limitations has run, they're in the clear.
The only counter to an SOL defense is to try and claim that the SOL was paused for some reason, but those exceptions are very narrow and wouldn't apply here (and in the real world very rarely apply to civil cases).