This isn't a paradox, the bomb will go off no matter what, assuming Omega is a perfect predictor.

Amusingly, this wouldn't seem like a paradox if something good was guaranteed to happen if Omega guessed right. Like if the problem was that you're locked in a box, and you can only avoid getting a million dollars if you do the opposite of what Omega predicts. Answer: "cool, I get a million dollars!" and you stop thinking. In the problem as stated, you're casting about for an answer that doesn't seem possible, and that feels like thinking about paradoxes, so you think the problem is a paradox. It isn't. You're just trapped in a box with a bomb.