A bad oxygen sensor will cause other problems such as rough idle, poor engine performance etc but the oxygen sensor being bad will not cause an engine to not start.
An engine should start without the oxygen sensor so if your engine is not starting it could be a fuel delivery problem, bad fuel pump, bad throttle position sensor, bad ignition coil or bad ignition module or a whole lot of other problems.
But the oxygen sensor will not prevent the engine from starting so it's not the oxygen sensor if your car is not starting.
Another thing to check is either in your trunk or under or near the drivers seat could be a reset cable or some other way to reset the fuel pump.
Most if not all cars today have a safety shut off for the fuel pump that can easily be reset but it can prevent the vehicle from being started.