The monorail doesn't start running until the park opens, so you'll be a few minutes away when the gates open and anyone there starts entering. That said, you clear the bag check and the ticket line before you get on the monorail, and it drops you right in Tomorrowland so you don't have to negotiate your way through the park if that's where you want to start anyway.
One word of warning based on our experience last month is that if the monorail has any problems, you are out of luck and will need to hoof it to the park anyway. We got on the first monorail of the morning, sat for a few minutes, then had to get off and walk to the park. That meant we wound up getting in 30-40 minutes after opening as a result.