Zac McEachran scored the opener in the 6-0 victory after just 13 seconds, as the midfielder charged towards the edge of the penalty area and smashed home.
The home side’s fast start continued on 12 minutes, when Jayden Carbon fired in a low cross for Walsh to tap in at the back post.
Just after half an hour had been played, the Hoops added a third goal when Carbon provided another excellent cross, and this time, Walsh headed in from close range.
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Ninety seconds into the second period, Walsh completed his hat-trick when he latched onto a Josh Ashby pass and burst into the penalty box, before burying the ball past George Burton in the Rovers goal.
Lewis Coyle scored arguably the pick of the bunch midway through the second half, when he curled a magnificent free kick into the top corner from 25 yards.
Summer signing Cardo Siddik went close to the sixth goal, before Walsh managed it with his fourth strike of the tie, when he once again raced clear, and this time, rounded Burton and rolled the ball into the net with eight minutes to go.
The test for the Hoops will be to replicate their goalscoring prowess shown in the FA Cup, when they search for their first league victory of the season at home to Peterborough Sports on Tuesday night.