As you would have noticed by now if you regularly visit YouTube in a browser, each and every video has its own identifier, as seen by the string of letters and numbers at the end of every video URL (e.g. ?v=gocwRvLhDf8).
Technology speaker and tinkerer Tom Scott (whose videos I almost always find interesting) poses the question “Will YouTube Ever Run Out Of Video IDs?”, given the fact that last time Youtube mentioned stats, it was something ridiculous like 400 hours worth of content being uploaded per minute!
Theoretically of course you could, but practically it is near impossible. Plus, YouTube lengthened the odds even more in their favour by using base64 numbers as identifiers, which as Tom so succinctly explains, packs a lot of data in a really small string!