Hey there. If this is your first time trying to launch Crysis 3 from the Origin client, try this:
Go to Origin, right click on the Crysis 3 square, click "Game Properties."
Under "Game Properties" make sure "Disable Origin in Game for this game" is checked.
After that, try launching Crysis 3. If it does not work, restart your computer, and immediately try again (you shouldn't have to redo the above steps).
Please come back to let me know if this solved your problem or not.