Pumping in the morning

Hello ladies! I am going back to work and trying to figure out the best morning routine. My 3 month old typically wakes up around 630-7 but I am going to have to leave the house by 620 to drop him off at my moms and be at work by 7. I have been pumping in addition to nursing 1 time every day which I feel has really been maintaining my supply so I am wondering what the best way to fit in a pump and breastfeed before work is gonna be. If I pump at 445 and then wake baby to breastfeed at 545 will there be enough milk for him? Or should I feed him at 445 and put him back to bed until it’s time to go and then pump after feeding? Ideally I’d like to pump first because I know I’ll get a lot of milk that way but I don’t want to leave baby hungry!! Thanks!