The New Douglas Park club host fellow Irn-Bru First Division side Falkirk in the William Hill Scottish Cup quarter-final on Saturday as they bid for their first last-four appearance since 1935.
May has already graced the National Stadium after featuring for current side St Johnstone in their defeat to Motherwell two years ago, and the striker is keen to make a bigger impact this time around.
He said: "I was lucky enough to get to a semi a couple of seasons ago with St Johnstone when I came on for the last half hour.
"But this is different as I am playing every week and I know that I am the central striker – there is a lot on the shoulders of the XI that start. We know this is a huge, huge thing for Hamilton.
"The Motherwell game wasn't a great start – I came on when it was 3-0 to them. At the age I was, I didn't realise quite what it was I was involved in and how big it was as it was my first season in football. Now I know what a massive game it is."
A semi-final appearance would give May another chance to showcase his talents to a wider audience, with the striker out of contract in Perth come the end of the season.
He said: "I'm just playing away for my future, wherever that may be.
"I've not spoken to anyone at St Johnstone about a new contract. But Hamilton is what I'm all about just now."