The Rambam says that through limud haTorah and through contemplation of the briah a person will come to have emunah.
While that may be the case once one accepts the premise that God does exist and that he gave us the Torah, the Rambam is explicit that this is not the case for someone who is searching by way of pure logic. He writes [and I paraphrase]:
The speech is fairly logical and straightforward. In order to disprove it, you would have to introduce some pretty shaky hypotheses including the DH.
I do not wish to debate the technicalities of the DH and I doubt the mods would allow it anyway, but suffice it to say that it is only because you have a prior belief of Torah miSinai that you reject the hypothesis. As SJS correctly pointed out there are logical ways around, and even problems, with that argument. As a matter of fact I recently emailed four problems I had with it to a prominent Rabbi in this field and I am currently awaiting his response. The point is that from a purely academic standpoint it would seem that the DH is very viable. It is only because of emunah that you reject it out of hand.
The creation of a paradox should still be within means of an omnipotent being, do you not agree?
According to the Rambam, this is a serious mistake. Again, I quote [paraphrasing]:
Let me just say that I agree to what SJS and Charliehall have been saying; I am just adding my piece.