Progress isn't exactly a quantifiable thing. You don't store a bunch of books in a library and call that 20 progress units per book. The world didn't slide back into ignorance when the library was burned.
There are certain things that were absolutely lost. Works of fiction, plays, speeches, and historical accounts were likely lost. Some scientific work, like botany and biology might have been rudimentary but they did have the chance to study plants and ecosystems that were different from what we know today.
But in terms of science and medicine I wouldn't say we "lost" stuff. We certainly lost records of what they studied and believed and the historical significance can't be understated. But since you asked about lost progress... No. Not likely. The tools and knowledge we have now would so vastly outstrip what they had or would even be capable of studying. We aren't missing fundamental pieces of knowledge because of the burning.
Basically the idea that the loss of the libraries caused some kind of backwards slide into ignorance and the dark ages, or that we'd be on Mars now if it weren't for those pesky razers is pretty ridiculous. We didn't lose plans for some ancient computer or hay powered rocket ship.
Piggyback: Do we know when the library was burned or did it happen several times?
This is my favorite response to this question: https://www.reddit.com/r/AskHistorians/comments/351kwh/how_serious_a_loss_was_the_burning_of_the_library/cr0ih75
(Although it doesn't have any numbers)
Most of the scrolls, books, and parchments would have copies elsewhere in the world especially if they were important records for royalty or financing.
I've also heard myths that most of the library was empty by the time of the sacking by Rome. Not because of fear but because bureaucracy had loaned or sold off most of them by then.
The loss of the library itself, if totally lost, would still mean the loss of many unique works. But it would be more akin to losing the Louvre or the Museum of Modern Art.
why is everyone so focused on the physical aspects of this event i.e. the loss of physical books. no one is commenting on the long term cultural significance of the event. a library is not just a collection of dusty papers, it's a cultural institution that promotes learning and intellectual curiosity. if one takes the physical event in isolation you could say it's not crucial, but the anti-intellectual movement that destroyed the library was hugely impactful to the academic world.