Two to three hours might be excessive, stay in bed a little longer. I get up about 3:15am for training and am at the gym about 4am / 4:15am. You can consume something like Gatorade 30-min prior to training and it will work well. I drink Gatorade to the tune of 68grams of CHO's and some BCAA's.
A couple good resources I've referred to for a class I'm in that helped me with my early morning pre-workout nutrition:
"An amino acid-electrolyte beverage may increase cellular rehydration relative to carbohydrate-electrolyte and flavored water beverages.
Nutrition Journal 2014, 13:47"
"Preexercise Carbohydrate Feeding and High-Intensity Exercise Capacity: Effects of Timing of Intake and Carbohydrate Concentration
International Journal of Sport Nutrition and Exercise Metabolism, 2014, 24, 258 -266
Â© 2014 Human Kinetics, Inc."