The term "warming up" sounds benign and comfortable, but when you do it you force your way through veils of resistance, some of them thick. It may actually hurt a bit.
It takes me at least 15 minutes of riding just to become functional, and longer than that to become fully operational. During that time, my legs feel stiff and heavy and my cardiovascular system chugs and misses like any cold engine.
The resistance does not begin at the first pedal stroke. It tapers up fairly quickly as I ride the short nuisance hills on the first part of my commute. It persists for at least ten minutes and tapers off quickly after 15. Depending on the day of the week and the warmth of the day, I may face further discomfort on the larger climbs further along the road.
You have to give it time. I can't warm up faster by going harder. Maybe you can. Experiment and see. But no matter what, you have to give yourself time to get going. This is true in any self-propelled activity, cycling, hiking, paddling or cross-country skiing. Get moving. Get yourself into it. Then increase the intensity to whatever level you have planned for the day.