Some of the best advice that you’ll ever receive on this subject was given to you by fearsomefour.
The actual game day should start you at least three hours prior to “scheduled” appearance. Your physical and mental framework is proportional to timing. By that I mean, first get accustomed to your surroundings, where the sun is, or isn’t, the environmental impacts that will impress your presence - heat or the lack thereof, humidity and so on. Start off by slowly building your mental and physical body to accept the demands of the day. Like fearsomefour pointed out, prepare. Remember, your arm is just an appendage that depends on the cooperation of your entire physique, a compliment if you will of progressive movement(s).
On the other hand, if you’re put into the field, then called in to relieve someone with only five(5) to eight(8) pitches as “thee warm up,” you’re pretty well done, even before you begin. So if that is a customary way of doing things where you are, there’s not much here that can help you.