They rely on artifacts and art. So yeah, it's quite possible the bow was invented earlier, probably a bunch of times in a bunch of places.

People are smart, but we're smart in pretty regular and repeatable ways.

9000+ BC - no arrow heads

8999 BC to present - butt loads of arrowheads

It just says they were invented in 9k BC. That does exclude them also having been invented in 10k BC.

Edit: *doesn't exclude
Sorry

They may have been mentioned/featured in things that last longer than the bows. Statues, pottery, writing on stone tablets.

Also I think they find skeletons with flint arrowheads in them sometimes too.

So it can be pieced together from lots of small, even partial data points.

But we find new stuff all the time that changes what we thought.

They found a 4000 year old bagless vacuum cleaner the other day.

That last one was a joke.

There’s always big error bars on these dates for that kind of reason. Actual archeologists are going to be careful with their language and say things like “the earliest evidence we have for bows is around 9000 BCE.”