Let's consider where the recent nominees have been 9 years prior to the election:
Mitt Romney | 2003: Newly-elected Governor of Massachusetts |
Barack Obama | 1999: State senator |
John McCain | 1999: Arizona Senator; running for President |
John Kerry | 1995: Massachusetts Senator |
George W. Bush | 1991: son of President |
Al Gore | 1991: Tennessee Senator; failed Presidential candidate |
Bob Dole | 1987: Senate Minority Leader; running for President |
Bill Clinton | 1983: Governor of Arkansas |
George Bush | 1979: Former CIA director; running for President |
Mike Dukakis | 1979: Former Governor of Massachusetts |
So yes, it does seem that it is likely that the 2024 winner would be one of the names you spot if you took a sieve of all the current Senators and Governors that would be within a plausible age range (Just a coincidence that the only three "unknowns" on that list ended up winning it all). Further, there is a good possibility that the 2024 winner is a candidate for President right now; or would be running for President if Hillary were not.
It's also worth noting that many of the last elections have been won by the candidate who entered major office last.
That's been the case in 1992, 1996, 2000, 2004, 2008 and 2012.
Also based on that list, the median half of ages were between 45 and 56. Thus, I think the criterion should be expanded to include names born after 1959. Expanding this criteria adds notable individuals such as Booker, Gillibrand, Baldwin, Klobuchar, and Bullock for the Democrats and Walker, Ducey, Sandoval, Christie, Martinez, Pence, Ayotte, Tim Scott, Paul, Flake, and Thune for the Republicans.