Could be a piece of firing pin retaining pin broken off and lodged in the firing pin channel that locked up the firing pin. Can you push the firing pin forward if you remove the slide, depress the firing pin block (push it towards the top of the slide)?
If the firing pin moves forward you should be able to see the tip of it come through the hole in the breech face. If not, could be a broken tip on the firing pin.
I've seen the firing pin return spring break (on a rifle) and jam the firing pin up in the channel.
You should probably get the right sized punch, remove the slide from the frame, remove the barrel/recoil spring/guide and drive that firing pin retaining pin out of the slide to inspect it. Install a new one (CGW or CZ Custom) when you put it back together, no matter what you find.
I've only had a couple omegas apart vs. the CZ75B types and right now I'm not picturing (in my mind) the way the firing pin block is lifted to allow the firing pin to move forward freely. If that firing pin will more forward and protrude from the breech face with the slide off the frame and you pushing the firing pin block up while pushing on the rear of the firing pin with a ink pen tip then the mechanism may not be fully lifting the firing pin block up out of the way when you pull the trigger. Never had that issue on an Omega so I'm not sure what would cause that (parts wise - fitting or function.)
Good luck with it.
If you don't want to fix it and it's new, call CZ USA and get them to e-mail you a return authorization form and shipping label to send it back to them (if you're in the USA).