Wits have been touted amongst the favourites to challenge for league and cup honours in recent seasons and show increasing potential each season.
However, the Clever Boys have only managed to lift one top flight trophy in the past two decades, after they beat AmaZulu 3-0 in the 2010 Nedbank Cup final.
Since Hunt took over the reigns at Sturrock Park in 2013, the three-time Absa Premiership winning coach has lead his troops ever closer to an elusive maiden league title - leading the club to a two third place finishes and a runner-up spot last season.
Wits, who have done good business in the recent transfer window, have again shown signs that they could challenge for silverware in the 2016/17 campaign, having already beaten the big guns in Kaizer Chiefs Orlando Pirates.
Hunt, though, admits that the pressure is increasing both externally and internally as he targets his first title with the Milpark-based outfit.
"I think there's pressure that come from the media, and we know we have our internal pressure," admitted Hunt.
"Obviously after beating Chiefs and Pirates in the first two games, everything gets bandied about in the media, but it's fine, we're quite happy and we know where we are.
"We want to achieve the goals we've set – whatever you want to call it. We don't want to get ahead of ourselves.
"It's the old adage – you're probably sick and tired of hearing this but, I mean – 'one game at a time', and that's all we'll try and focus on."
After starting well last season and showing early signs that Wits were the team to beat, only to then stutter towards to end of the campaign, Hunt concedes that it's about time they get something under their belt and is willing to win any trophy this season.
"You have to look at where we started – the base. When I first came here, where we were and where we are now, we've won nothing and we've done nothing," he added.
"But we've made good points in the last three seasons and we got into one final [2014 Nedbank Cup against Orlando Pirates], which we lost. We need to stop doing something and start achieving.
"But if you look at Mamelodi Sundowns, SuperSport United, Chiefs, Pirates... These teams have won many, many trophies, and this club hasn't got a history of winning trophies.
"We need to create that culture and the feeling about this place, and then you'll see it will be much easier to win trophies.
"I think at this point in time anything for this club is good – even if we win the milk cup on a Sunday morning - anything. Even if we win a friendly tournament.
"We can't pick and choose. Sundowns, SuperSport, Chiefs and Pirates can pick and choose, not us."
Wits will host City at the Bidvest Stadium on Saturday evening, before travelling to Cape Town for the return leg a week later.