As Capt says, a flight has a flight plan with an EOBT (estimated off blocks time). You cannot start up over 15 minutes before or 15 minutes after that time. So if you are ready to go, you have to wait. This time cannot be bought forward only delayed so asking if you can go earlier will get a negative response. The only way around it is to cancel the flight plan and refile for an earlier time. The risk with this is that you may then get a slot as you have dropped out of the system and then you are joining at the back of the queue. All the info is on the Eurocontrol website and is to avoid the need for more flow than is normally required.
Now if the airport is ACDMed, that's even more/less complicated depending on your point of view.