Congratulations, it always make me happy to hear that there are new bike commuters! The more bike commuters there are, the better chance we have at improving cycling infrastructure and making things better for all bike commuters.
You will adjust to your current gearing. I recently made the transition from MTB gearing on a former commuter bike to compact double gearing on a road bike for commuting. The things that helped me with this were: 1) starting with rides that had minimal hills and/or hills with low "grades" of steepness. I have been gradually "upping the ante" in terms of grade steepness; 2) using a trainer or stationary bike at the gym to do interval training once or twice a week. I have been amazed at how much this helps me. Last winter, I wasn't able to ride as much as I wanted, but I did make sure I did intervals at the gym at least twice a week. When I got back into doing some of my regular rides, I found that the time it took me to complete the rides was significantly faster after just a couple months of gym workouts where I spent 20 minutes twice a week doing intervals before weights.
Regarding training, don't have a gym membership but I thought about buying a trainer to build up my strength/stamina but given their price is a little steep - I will use the local hills with lower grades of incline as my trainer for the time being.
you'll get better on that hill. research how to nutrify before you leave work.