During the season 15 premiere, Williams, who was wrongly convicted of a 1983 crime, sang Elton John's hit song "Don't Let the Sun Go Down on Me" to a roaring live audience and viewers at home who learned of his story.
"It was awesome," Williams, who watched AGT while in prison, tells PEOPLE of seeing his audition on TV at home with his family members.
In 1983, Williams, who was 22 at the time, was convicted of aggravated rape and attempted murder in Louisiana. Fingerprint evidence did not match his own, and witnesses testified that he was at his own home the night of the incident. However, Williams was sentenced to life in prison without the possibility of parole.
At the 12-year mark of his prison sentence, Williams reached out to the Innocence Project with a request for the organization to exonerate him. Thanks to years of their hard work and new fingerprint-matching technology, Williams' case was overturned due to the fingerprints found at the scene of the crime matching a serial rapist.
After being incarcerated for more than 36 years, Williams was released from prison in March 2019.
"I'm still trying to believe all of this," he says of his newfound fame after his audition amassed millions of views worldwide. "I'm still pinching myself if this is not a dream."
As for his song selection, Williams says "Don't Let the Sun Go Down on Me" has a special meaning. "I've always been a fan of Elton John's. The song related so much to my story. I always took that as a personal song," he shares. "I always said once I get the chance to sing that song, that would be the song."
Williams' audition was released on YouTube ahead of the season 15 premiere, and caught the attention of John himself.
"He called me personally. He gave me an invitation to sing on his show when he comes back to the United States. It was definitely a surprise!" Williams says of their phone conversation. "He said he never heard anyone sing his song like that ever. It was really touching to him. It brought him to tears, he said. It was touching."
John also tweeted his reaction, writing, "I was moved to tears when I heard Archie's story and saw him perform 'Don’t Let the Sun Go Down on Me.' The courage and forgiveness shown by him is truly inspiring. The same spirit that the world found so inspiring with Nelson Mandela."
A day after his audition aired, Williams says he's "overwhelmed with joy" to know his performance and his life story have touched so many.
"I used gospel music to reach out to people, mostly my time in prison," he explains. "When I first got there, I got me a band and I started to reach out to people there with my music."
And now he's hoping to help others who sent "so many comments from all over the world, not just the U.S.." Soon after his performance, Cowell joined the Innocence Project as an ambassador.
"That's the best that could've happened to us," Williams says of Cowell using his platform to expand the work of the Innocence Project. "Because it'll help other guys in prison and it will help. There are guys in prison whose cases the Innocence Project is not allowed to take because evidence still has to be tested. Those guys are just as innocent as me."
Williams hopes the attention garnered by his audition will open doors for more "access and tools to be able to try cases like mine," adding, "Simon is the biggest access we could've ever had for me and the Innocence Project."
Though he's received messages from fans who've said he's "changed their lives," Williams still has his eye on the $1 million prize.
"My main goal is to win, I know I'm going to win. I'm confident in that," he says.
America's Got Talent airs Tuesdays (8 p.m. ET) on NBC.