The Highlanders and Southland first five-eighths and partner Miriam on Saturday welcomed baby Milla into the world.
Sopoaga was a late withdrawal from the All Blacks' trip to Argentina for next weekend's Rugby Championship clash against the Pumas, replaced by Beauden Barrett who had originally been slated for a rare week off.
All Blacks coach Steve Hansen confirmed on Friday before flying out of Auckland for Buenos Aires that Sopoaga would almost certainly join them in Cape Town for the following weekend's Rugby Championship finale against the Springboks.
"If I have to wait another 799 days to start a test match ... I tell you what, the gift I was blessed with today is well worth it," said Sopoaga on Twitter.
On Instagram, Sopaga posted a photo of his newborn with this message: "For all the things my hands have held the best by far is you. Welcome to the world Milla, your Mum & I Love and adore you."
Sopoaga would have started at No 10 for the All Blacks in Argentina had he made the trip, which would have been his first appearance in the run-on XV since he started his test debut against the Springboks in Johannesburg on July 25, 2015.
His 10 test appearances since then have all been off the bench.
Barrett said on Friday he had been fully prepared for the late callup, which came on Thursday night, and supported Sopoaga in his decision to prioritise for his baby's arrival.
"Obviously family comes first and it's exciting for Lima," Barrett said.
"If I was in his position that's exactly where I'd want to be expecting my first child."
Photo by: NIGEL MARPLE/REUTERS (Caption: All Black Lima Sopoaga is a father after the arrival of baby Milla into the world)