A packed schedule has seen Arsenal face the likes of the Bayern Munich and Chelsea in Asia, while they are currently preparing to play two fixtures in the Emirates Cup this weekend.
That will be followed by the Community Shield against Chelsea, and Walcott feels that there can be no excuses for anything other than a positive beginning to the new top-flight campaign.
The 28-year-old is quoted by The Mirror as saying: "We've lost the opening game of the season over the past few years I think, so we need to make sure that pattern changes this year.
"We're playing against strong teams in all the games we're playing in pre-season, so there's no excuse for a slow start. This team's had ups and downs but we need to start well first. Starting well is the main priority and then we've got to push on from there.
"The manager has said that right from the first day here — make sure there's a fast start. That's why it's important for us to play these bigger teams in pre-season, to be mentally ready and switched on."
Arsenal begin the season with fixtures against Leicester City, Stoke City and Liverpool.