Is it damaging to a hybrid's gasoline engine to let it rev high before it warms up?

Generally, it is not a good idea to let an engine reach high RPMs when it is cold. The potential issues with a cold engine under full throttle are well documented.

I have a Fusion Energi and the car works in EV mode until the battery is depleted enough, but it can use the gasoline engine when it needs more power. What I notice happening is I drive for several miles until I reach a significant incline and the gas engine kicks in to help it up the hill. Since it has a sudden need for power, it turns on and immediately revs high. Given the electric motor has a separate cooling system, I do not believe the gas motor has a chance to warm up at all, not to mention having operating temperature oil, when it has been off up to that point in the drive. Unfortunately, this happens basically every day on my commute, it is not rare.

Can this damage the engine or reduce its life significantly?

I could let the car drop by about 10 miles per hour on the incline by staying in EV mode, but I risk causing a small case of road rage behind me.