The visit of Mike Mulvey's Roar to the 7000-capacity Macedonia Park in the Perth suburb of Balcatta on 19 August is the pick of the round of 32's minnow versus giant duels and Williams - a Perth policeman - is aiming to roll back the years to the mid-1990s when unfancied Hitchin reached the second round proper of the FA Cup by claiming the scalps of Hereford United and Bristol Rovers.
The fun ended when it lost to Wycombe Wanderers, managed by now Ireland boss Martin O'Neill, and Gillingham, led back then by now Crystal Palace chief Tony Pulis.
"We will be testing ourselves against the best in the country and had I been given the choice this is the tie I would have picked," said Williams.
"They have a reputation for attractive football and we will have nothing to lose. To be at home in front of our own fans is just an added bonus and we are hoping for a near full hose of around 7000.
"We play in front of average crowds of around 400 so it's going to be a special night."
The defending National Premier League champion in Western Australia, Stirling is the club which spawned the talent of Socceroos great Stan Lazaridis as well as Daniel de Silva, the 17-year-old Perth Glory rookie who will join AS Roma in Italy in a year.
It was also the club which gave gifted former West Ham United and Young Socceroos striker Dylan Tombides, who tragically died earlier this year, his start in football.
One-time striker Williams, who also played for non-league Hayes and Bedford Town before migrating to Australia in 2003, added: "We have a good mix of players and we believe we have enough quality to worry Brisbane."
Williams is looking to former Perth Glory rookie Moses Kalau, a Congolese refugee, to provide the spark up front down the left side, insisting his pace can hurt Brisbane.
Goalkeeper Aleks Vrteski is a former Australian youth player who played four first-team games for Perth Glory, while midfielders Dave Micevski and Dean Evans were also on Glory's books along with defender Hayden Doyle.
"We'll give Brisbane the respect they deserve but there's nothing to say we can't pull it off on the day. We'll be putting in extra training sessions to try and prepare the players," added Williams, 45.
"Our aim is to give ourselves every chance against the top players in Australia. It's a great opportunity to get the romance of the FFA Cup up and running.
"We want Brisbane to look at us afterwards and say 'they have got some really good players there'.
"Myself and my assistant Daniel Stoitis encourage an open and expansive game and try and keep the ball down and play. It's been a bit of a rebuilding year for us after losing the core of our team at the end of last season, players like former English Premier League player Andy Todd who went home.
"It's all about giving ourselves a financial boost and putting this club on the map in terms of recognition. It's an opportunity we plan to make the most of."