That can give you some indication for your problem
1) fuel starvation, it could be that the fuel pump is not delivering the fuel necessary to start the engine, when you press the acceleratior more fuel goes into the cylinder and thats why it starts
2) bad or dirty MAP sensor, not correctly detecting the air pressure going through the throttle body, thus supplying less fuel into the cylinders. are you getting good fuel economy? (+13km/ltr in city)
3) dirty plugs or worn out plug cables
4)low octane in fuel. Low octane fuel detonates faster then hi octane fuel so it detonates before the piston reaches top dead centre and thats why engine vibrates on low idle (premature combustion chamber explosions) the ecu tries to compensate for these but depends of the data given to him from the knock sensor
5)low battery cold start amperes. The engine needs a good kickstart especially when cold. If it is not getting this it will take longer to start
Ignore 02 sensors at this stage because the ecu starts the engine at what is called open loop (it does not try to deliver a lambda value of 1.0 or 14.7:1 air/fuel ratio) because 02 sensors don't deliver data when cold, when they are hot enough (very hot) they start to deliver voltage variations to ecu, then ecu goes to close loop but it can take 2-3 minutes ecpecially with non heated sensors
@imrananr .. Thanks!