"It's just made me look at things in a whole different light. Sport's sport. Sport is not everything.
"My biggest challenge for myself is to be the best father I can be and be the best husband I can be.
"That is just an awesome feeling. It's the best. Changes your life."
Williams said he had the "thumbs up" from All Blacks coach Steve Hansen to return to Auckland for the birth but his wife Alana told him to remain with the squad in Cardiff.
"I was coming back and she just told me to stay. She's the one that actually made that decision," he said.
"Yeah, it was tough seeing the birth via Skype. It just made me even love my wife even more than I already did, and appreciate her more because obviously it takes a strong woman to tell her husband not to come back for the birth.
"Seeing my daughter for the first time after I came back from the tour was just a life-changing experience... it still blows my mind."
Williams admitted nothing could have prepared him for fatherhood.
"Beforehand you think 'oh, changing nappies, I'm going to be up, I need to get sleep for training,"' he said.
"But when it happens, when you're there, as soon as you hear a wiggle or a cough or something, you're up straight away. It doesn't bother you."
The 29-year-old said Imaan had given him the drive to become an even greater sportsman.
"I was never going to be a rocket scientist," Williams said. "But I found the field that I was blessed to be able to do and I just put my whole effort into that.
"Now boxing, I may not be the best boxer in the world but I try my hardest and obviously I can use my daughter as a motivating factor now."AAP