It’s doubtful that the oxygen sensor is contributing to your hard starting problem. The O2 sensor doesn’t come into play until well after the engine is started. When you start your car, the computer is excluding some of the sensors from the mix, including the O2 sensor. After the engine has been running for a while, and the O2 sensors have heated up to the correct temperature (which they need to be at to give accurate readings), then the computer ‘goes for it’ and puts the engine in “closed loop” mode, where the O2 sensors determine the fuel mixture based on the remaining oxygen in the exhaust gases, indicating whether the combustion process is efficient or not. So to sum up, O2 sensors have no role in staring the engine.