After being booted out by West Bromwich Albion as a teenager, the Wales international played part-time before working his way back up the ladder.
Williams, 27, said: "What's strange for me is that I used to think that Stafford Rangers was a big game when I was playing for Hednesford.
"Now, it's Manchester United. But you just adjust to it.
"We are getting used to big games at Swansea, but this is different. We deserve to get excited by this."