The League One club stunned Premier League leaders Chelsea with a 4-2 victory at Stamford Bridge in the fourth round and were rewarded with a clash with another top-flight outfit.
As deputy to regular number one Jordan Pickford, Williams is ready to assume his FA Cup role once again and warned of the impact the victory over Chelsea has had.
"I look forward to all the cup games because obviously it's my chance to play but with the atmosphere, the crowd, the occasion, it's going to be a brilliant day," he told Perform.
"The boys have been really calm about it, no-one's under the illusion that this is going to be an easy game, we're going to have to really focus probably more so than we did for the Chelsea game.
"Sunderland will be wary of what we achieved and they'll approach the game as they would any other and it's up to us to match that and make sure from the first whistle that we're good to go."
Bradford have taken five points from nine since victory at Stamford Bridge and go into Sunday's clash after beating high-flying MK Dons on Monday.
While Sunderland lost to fellow strugglers QPR last week, Williams is not reading too much into the sides' form.
"They're Premier League opposition with world-class international players, it doesn't matter what form they're in, they'll be a very difficult team to play against," he added.
"The good thing for us is that the recent run of results gives us self-confidence going into the game and we just have to make sure the performance is right."
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