With the physical evidence, science can demonstrate beyond a reasonable doubt the world is that old. There are a few points, that aren’t show-stoppers, that haven’t been worked in to the theory, but young-earth Creationism requires much more mangling of the available data than straight Atheistic science does.
However, God creates the physical evidence, so it’s possible it’s not (this is the “last tuesday” argument, or what was popularly called the Omphalos Hypothesis in the late 19th/early 20th centuries, but has been largely rejected by creation scientists today). However, God is a God of Truth, not of confusion, so I don’t think he’d place dinosaur bones around just to confuse us.
However, God works in mysterious ways.
And, I do count myself a creationist, of the “Old Earth” or a modified “Theistic Evolution” variety (i.e. I believe God caused the big bang, and Man did not evolve from ape, at least not through any natural means, and was created, separately from all other creatures, as a unique image and likeness of God; I reject abiogenesis and macroevolution; I reject common descent as it pertains to man, but accept it as it pertains to lower animals, but accept microevolution, etc.).