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The absence of proof does not mean that proof does not exist somewhere. It just means we haven't found it yet OR it really doesn't exist. Like you said, time will tell.
In the case of the Oort Cloud there are very good reasons to think that the cloud is there but hasn't been found yet.
Firstly we have solid evidence that the Earth and the Solar System really are old.
Secondly, all that is being proposed is that the Solar System stretches out further than the furthest observed object. There's no good reason to suppose that there is a sudden "stop" rather than more gradual "thinning out" of material that is proposed.
Thirdly we have observed objects in the Kuiper Belt (which is more important for the short period comets that the Creationist argument deals with anyway).
Fourthly comet nuclei at that distance are incredibly difficult to observe. There is no good reason to think that we would have seen them yet.
Because of the evidence of age we can't simply discard the idea, we must look at reconciling the evidence. The Oort Cloud is a highly plausible hypothesis given the evidence that we do have. It is not nearly so plausible that all the evidence of age just happens to be wrong (check out RAZD's thread on correlations). So the rational conclusion is that the Oort Cloud does exist. Even if it turned out that it did not then we should still have to consider alternative explanations (maybe involving the Kuiper Belt) before concluding that the Earth was young. Only someone driven by the conviction that the Earth was young, and looking for excuses to reject the evidence, could think otherwise.