The Scarlets centre made his Test debut against Georgia at Parc y Scarlets last November in a game played behind closed doors.
This will be the first time the 25-year-old will get to experience a sold-out Principality Stadium as a player, but he has plenty of memories as a supporter.
Williams was in the crowd during Wales’ famous Haka stand-off in 2008 and he can’t wait to make new memories as a player.
“In 2008 I was a young lad but I was there in the debentures with dad,” said Williams.
“I just remember the crowd, once we realised what was happening. I was young, I can’t remember how old I was then.
“I just remember once we realised the All Blacks weren’t moving and the referee was telling everyone to get back 10 and start the game, the crowd just jumped on top.
“I just remember the noise and the atmosphere was ridiculous. And it set it up for the game then.
“I’m looking forward to the weekend now.
“This is going to be the first time most of my family are going to watch me play for Wales. It almost feels like a first cap, in a way – that real special moment playing in front of fans at the stadium with such a tough challenge ahead.
“It’s going to mean the world to have all my family there supporting me at the stadium in front of a sold-out crowd. It’s going to be big.”
Williams missed out on winning more caps last season after suffering a shoulder injury against Ireland and he hopes to make up for lost time.
Despite New Zealand being overwhelming favourites, Williams believes Wales can give a good account of themselves.
“It is just about backing ourselves,” said Williams.
“It is not so much about what has been and the challenges we have got to face, it’s about this group of players and having a job to do on Saturday.
“We have got to win a game of rugby at the end of the day, it doesn’t matter who it is against. We all know our roles, we are all aware what the occasion is, and we have all played enough rugby.
“It has just been about us and focusing on delivering on the weekend. I have been back two games but I think I’ve played well. Confidence is good personally and it is about seeing where we are.
“We have trained well and we are really looking forward to being back at the stadium in front of a full crowd.
“We are all aware of the challenge.
“It does not matter who or where you are playing, we are all professionals so it’s just about doing what you are doing with the regions and stepping up 10 to 20 per cent on top of your game to play for our country.”
