I have had exactly this argument before and this has always been my issue with the claim. I recall people saying this about music when I was in college, an example I find especially frustrating because, per my friends argument, all contemporary music is influenced by, say, Bob Dylan, the Beatles, 'the greats' etc, and nothing new can truly be created in the shadow of these classics. It's nuts because it ignores all of human civilization up to that point, and doesn't give credit to people in the present day for being able to be original.

But I think the way you have put it here is more clear than anything I've been able to manage. I think I put it in a more extreme form, which is to say that the earth had no life on it for ~3 billion years, and still no humans until ~100k years ago. At some point the first music was made. And if it could be original then, whatever it was that made that possible, should presumably make it possible now, too.