The thread is “Timing for driving to Epcot (for early breakfast)” so the first question is "Driving from where?"
Next question is “Which restaurant?” though I’d suspect it’s Akershus.
That will determine how long a walk you’ll have once you’re in the gate.
Anyway, out at the toll barrier there will only be a couple lanes open, but there isn’t going to be a huge amount of cars an hour before rope drop. But once inside the lot, don’t automatically assume you’ll be given the closest parking spots.
Also, bear in mind with Dana’s suggestion about parking at one of the hotels.
Swan and Dolphin charge and Boardwalk’s self parking lot is across the street, next to the Hess station. So if you’re going to do this, park at the Beach, but use the excuse that you’re trying to get a walk up to Cape May for breakfast.
I’d guess with kids and gear you should arrive 60-75 minutes early when parking at a hotel or at Epcot’s guest lot.