With a hybrid you have to get your head around the start up process as "power on" just like your phone or computer. When you turn the key or press the start button (whichever it has), a light comes on the dash that says "READY". That is your cue to put it in gear and go. In the "power on" process the gasoline engine may or may not fire up, that's up to the computer based on a number of variables.
Once you are underway, the computer is constantly orchestrating whether to use the gas engine or electric motors or both. Thus at times you will be under power from the gas engine only, the electric motor only or both- sometimes neither if coasting.
Things like the AC will blow cold and work regardless of whether the gasoline engine starts up or is running because hybrids have an electric heat-pump type of system not dependent on an engine driven compressor. Usually, the only reason the gasoline engine will start up immediately when you "power on" your car is if the hybrid battery is low or the exterior temperatures are at an extreme that requires high load HVAC use.
Just wanted to correct a couple of things here. I realize you probably just misspoke but I don't want anyone to be confused, though I'm probably adding more confusion.
First, I don't know what specific equipment the Maverick has but can make some guesses based on previous Ford products and info which has been shared previously. Some of that info may prove to be incorrect.
The Maverick will likely have a conventional style A/C and heating system for the passenger compartment, with a couple exceptions from other lower prices Fords. It will not have a heat pump, a system used mostly on small diesels and only for heat since the engine generates little heart at idle. Jeep liberty diesel comes to mind. Anyway...
It will have a conventional A/C compressor but driven by electricity, not a heat pump type system. It's a regular old compressor, except variable and electricity driven. It may be driven by either the engine or electricity as those do exist (ecu decides which drive to use, electric or engine based on inputs yada yada) but I'm guessing on this application Ford will go the cheaper route and it will be strictly electric.
It will also probably have an electric pump which continues to circulate engine coolant through the otherwise conventional heating system when the engine is off. In very cold temperatures the system commands the engine to run based on coolant temp, which will be one reason your hybrid economy really sucks in winter. It may have an actual electric heat pump to maintain temperature, but those things take a lot of power to run, so I'm guessing Ford went the cheaper route and will simply use the efficient Atkinson cycle engine for heat.
But as always, Ford may surprise us and use some totally different new thing. We'll just have to get our hands on it to see.