When a car is cold, you want the fuel mixture to be rich on startup......when a vehicle is warm, you want the fuel mixture to be lean on startup....
O2 sensors have nothing to do with startup.....
I would suggest getting a gauge on the fuel system to see what the pressure is and if it holds.....
Would also suggest getting the system scanned for codes and to observe the coolant sensor data, to see if it is reading correctly.....