There are numerous examples of wood having been preserved for millennia, in the right kinds of conditions, typically an anoxic (oxygen-free) environment. Even Otzi the Iceman, the world's oldest known mummy, was found with a wooden bow and arrows. There is no mystery here about how the wood was able to survive being frozen in a glacier.

Wooden objects from Ohalo II (23,000 cal BP), Jordan Valley, Israel

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Abstract
Eight wooden objects were found at Ohalo II, a submerged and well-preserved site in the Sea of Galilee, Israel. The fisher-hunter-gatherers' site has been radiometrically dated to 22,500–23,500 (cal BP) with 45 assays read by four laboratories. The wooden objects were found on brush-hut floors. They include a bark plank with polish and use signs, pencil-shaped specimens with longitudinal shavings, and other types that may have been decorative or symbolic. One incised wooden object is identical in size and incision pattern to a gazelle bone implement found in a grave, behind a human skull. The recovered wooden objects are not directly related to hunting, gathering, or fishing, and frustratingly, there are no remains of bows, arrows, spears, handles, or other such items. Nonetheless, the objects present a wide repertoire in terms of size, shape, and possible function. The new finds add to the growing body of evidence concerning the use of perishable materials during the Upper Paleolithic.

Accepting these facts does not have to mean you reject the existence of God, SoSick. Surely God would have intended for people to use their intelligence and directly engage with the evidence we find, rather than dismiss it, ignore it, or call it lies? Wherever the evidence may lead us, surely there can always be an underlying belief that God created it all?