Ranked eighth in the world heading into the showpiece event, Jason Holder's promising side sent out a statement of intent in beating 2015 finalists New Zealand by 91 runs in their final warm-up game on Tuesday.
"It would be great if we could create our own legacy. Obviously, Chris has done that in the Test and ODI format, and then is 'Universe Boss' in T20 as well. The young guys like Shai Hope are aspiring to reach the heights that Chris has reached," the 30-year-old was quoted as saying by the ICC.
"If we can win, we can be looked upon in the way that the team of '75 and '79 was looked upon, as heroes of sorts.
"Once we do the things we're supposed to do, often we should go far enough in the tournament.
"It's one of our better chances in the last 40 years or so to win the World Cup, so it's time for us to show up and show off.
"On our day, in semi-finals and finals we have some guys who can win it on their own."
Put into bat first on a near-perfect batting track Tuesday, stalwart Gayle plundered 36 from just 22 balls to lay the platform, with Shai Hope then adding a century as part of a mammoth total of 421 - their biggest ever in a one-day game, albeit not an official ODI.
An icon both globally and in his own dressing room, the prolific Gayle will no doubt be integral to his side's chances of glory.
But without a semi-final appearance since 1996, Brathwaite feels others must step up to the plate as the 1975 and 1979 winners go in search of their third World Cup trophy.
With scores of 300 now commonplace in ODI cricket, much of the talk in the build-up to the competition has centred on whether Holder's men have enough firepower in the bowling ranks to make their mark.
All-rounder Brathwaite though, who took three wickets in Bristol, believes his teammates have all bases covered when it comes to taking wickets.
He added: "I don't think there will be much stymying the flow of runs in this competition. Everyone will be looking for 320 plus, so it's about getting wickets.
"We've got two guys that bowl 90mph, a left-hander that swings it back, someone who is very skilful in (Kemar) Roachy and in Jase (Holder) he presents something different, bounce and movement, with the new ball as well, so the bowling attack is covered.
"We've also got two spinners, so it's just about coming together and finding a way to attack."