Now I'm inspired to try to fill out this list...

Pegasus (company's first try overall), Antares, all of the Minotaurs, Atlas 3 and 5 might count as new... Epsilon, H-2 (new?), Vega, Ariane 1, 3 & 4... And the Ariane 1 is both totally new on a systems level and an institution's first attempt at building one. Long March 5, 6 & 7.

Of the investor-backed launch startups, I think it's either no company got it first try... or Orbital Sciences counts as making it first try with Pegasus. Not sure if they count as an investor backed startup.

SLS? It not only made orbit but also got it's payload around the moon. While it used many previously proven technologies (and it even previously flown engines), those were either modified or combined in previously untried ways, enough that I'd call it a new vehicle for the purposes of a flight test.

Speaking of previously proven technologies... the Space Shuttle made it to orbit on it's first launch attempt as well... with crew.

I think it is no company has reached orbit on first attempt. But they have been successful on later rockets. This includes SpaceX which was blowing up rockets phase with Falcon 1 but were successful with Falcon 9.

Zenit-3SL, Angara, Saturn family.

Falcon 9? SLS? STS?

Falcon 9 did.

Juno did just fine.