No comment on the bow per se, but on Pangaea and us...
Pangaea began to break up around 200 million years ago. The dinosaurs went extinct 65 million years ago. This is why we see such a wide dispersal of nearly identical dinosaurs from the Triassic to the beginnings of the Jurassic periods (230-200 million years ago). We as a species (homo sapiens sapiens) came about only around 200 thousand years ago (Omo remains dated at 196k years old).
Also, while Pangaea was together, the NE coast was China, and the west coast was North America. They did not touch each other at any time.
As for a Chinese type bow in the Pacific near America- could have come from anywhere- the Chinese did sail alot way back when, and the dating could very well be suspect, as carbon dating is not so good for younger finds, as well as the sea bottom containing differing amounts of Carbon-14 than the majority of dry land, which can throw off the dating by principle.
Also, Neanderthals were known to exist along side Homo Sapiens, and we have even now shown through DNA testing of Neanderthal remains that we modern humans have Neanderthal genes. But, the youngest known Neanderthal remains are 32 thousand years old, though there is fire evidence in Gibraltar that suggests some Neanderthals were around as late as 24 thousand years ago.
Whew.
Neanderthals did not use bows, they used spears, and big, beefy spears at that. We are here largely in part to our (Homo Sapiens) use of smaller diameter spears that were much better for distance hunting. Neanderthals were stronger than us bodywise, but even they could not throw their spears with any aim. The spears they used were more of the pike type for close-in hunting. Dangerous stuff, hunting mammoths close up...
