Only charging battery from outside will not do it.
The catalytic converter needs to be warmed up too.
The car will run the engine until the catalytic converter (CC)
goes up to a predetermined temperature so that the car
conforms to the smog emissions requirements.

Now if you put an electric heating coil around the CC and heat
it from the plug, that will solve this cold start problem.

I have noticed that when I do pulse and glide for a long
time in cooler temperature around 50F, the engine comes
on even though the battery shows good charge. This must
be because enough hot exhaust gases are not going through the
CC to keep it in its specified temperature range.

My mpg suffers terribly due to this. If the car could start
straight away in EV mode always, I sould have crossed 45 mpg
by now. I am still at 38-39.