I have been able to kill quite a few good bucks (all with bow), in NH, over my lifetime. I have not killed a single, mature buck, before November 1st. I hunt the early season to keep tabs on movement patterns, doe groups and general surveillance.
In late October, I will usually start to see an increase in daylight activity of bucks. When I start to see that, I hunt as much as I possibly can.
My most productive window is between November 9-14. Even thought the gun season is in full swing, thats when I have killed the most bucks.
Like David said, hunt remote, overlooked and unpressured areas. I try and be a ghost. Scout like I am hunting. Check cameras like I'm hunting. Find access that will not take you through deer movement. And, only hunt on the correct wind.
Good luck!
Seth