To the best of my knowledge, there is currently no canon description of a successful break-in at Gringotts prior to Quirrell in Philosopher’s Stone. However, it is implied that this probably isn’t the first. This is Ron, telling Harry about Quirrell’s break-in:
“Did you hear about Gringotts? It's been all over the Daily Prophet, but I don't suppose you get that with the Muggles — someone tried to rob a high security vault.”
“Really? What happened to them?”
“Nothing, that‘s why it's such big news. They haven’t been caught. My dad says it must've been a powerful Dark wizard to get round Gringotts, but they don't think they took anything, that's what's odd. 'Course, everyone gets scared when something like this happens in case You-Know-Who's behind it.”
— Philosopher’s Stone, chapter 6, The Journey from Platform Nine and Three-Quarters
The fact that it’s “big news” backs up what we’d expect: that this is a rare event, but if it was the first, then I think that would be even more remarkable.
So this probably isn’t the first.
We know Quirrell probably couldn’t have done this alone, but was being aided by Voldemort. If Voldemort can assist a break into the Bank in his severely-weakened form in Philosopher’s Stone, then I see no reason to think that he couldn’t be able to do the same at the height of the First Wizarding War. Of course, that doesn’t mean that he did, but it would be unsurprising had he done so.