A lot of caffeine advice says wait an hour after waking up before your first coffee. The reasoning comes down to cortisol.
Cortisol, your body's natural wake-up hormone, is naturally high in the first 30-60 minutes after waking. Caffeine and cortisol work through some overlapping pathways, so having caffeine while cortisol is already high may mean you're not getting as much out of that first cup as you would slightly later, once cortisol has started to come down naturally.
In practice, that means a coffee closer to 60-90 minutes after waking, rather than the moment you're up, may make more sense for a lot of people's routines — though everyone's cortisol rhythm shifts a bit with sleep timing and lifestyle.
If your morning doesn't allow for a coffee break exactly on that schedule, a piece of gum is easier to time precisely than making a full cup. Neuchu's 50mg per piece works well for that. You can find it here.