According to the Ventura County Sheriff's Office, Rivera arrived at Piru Lake in Ventura County, California, north of Los Angeles, around 1 p.m. PST Wednesday.
She hired a boat and she and her son were seen going out together on the lake, said Sheriff Captain Eric Buschow at a press conference.
About three hours after leaving the dock, another boater on the lake discovered a boat drifting with the sleeping child on board.
The boat was found in the area called "The Narrows" at the north end of the lake.
Authorities were notified and they began search and rescue efforts from the air and with a diving team.
Buschow said that it was difficult to obtain information from the child, who told them that they had gone swimming, but his mother did not get back on the boat when he did.
The child was wearing a life jacket and an adult life jacket was found on the boat, according to Buschow.
Extensive research
The search and rescue mission was suspended Wednesday evening and resumed first light on Thursday.
Officials said more than 80 people were involved in the search for Rivera, best known for playing Santana Lopez on the hit Fox series "Glee", which ran from 2009 to 2015.
The lake was closed for research.
"Several professional search and rescue teams are actively searching Lake Piru for clues to the location of Naya Rivera. With more than 80 people involved in the search right now, we are using helicopters, boats, vehicles all - ground and ground staff to try to locate, "tweeted the Ventura County Sheriff's Office.
Authorities announced on Thursday that the operation had moved from a search and rescue mission to a search and recovery mission.
"We assume that an accident has occurred and we assume that it drowned in the lake," said vice president Chris Dyer at a press conference on Thursday. "We hope for the best, we prepare for the worst."
He said it is not uncommon for visitors to visit the lake mid-week as the draw is likely to be fewer people and less traffic.
The boat rented by Rivera was a pontoon boat with deck cover and the rental operator did not notice anything extraordinary, said Dyer.
The boat was found at the north end of the lake where the wind is often a factor in the sailing conditions.
Dyer stated that the depth of the lake can range from 6 to 40 feet and that the bottom of the lake contains a lot of debris.
He also said that Rivera's son was healthy and in family.
Security video
The Ventura County Sheriff's Office tweeted a link to a safety video posted on YouTube on Thursday.
The video shows Rivera crossing the lake parking lot, her son trailing in their wake, as the pair heads for the dock, to the boat they've rented.
They then leave the dock and head north in the boat on the lake, watch the video.
Officials have also tweeted the call to 911 in which an employee of the boat rental company reports the disappearance of Rivera and the discovery of her child.
Hope and despair
Celebrities and fans have been talking about Rivera on social media since the news of her disappearance.
There was both sadness that she perished and the hope that she would be found safe.
"I hope against all hope ... it was just a big joke and she will appear somewhere laughing with all her heart," tweeted Iqbal Theba, who played the main Figgins on the show.
Singer and actress Demi Lovato, who played one of Santana's friends, Dani, on "Glee", also tried to stay positive on Twitter on Thursday.
"I don't tweet often but sometimes my tweets come true so let's demonstrate together on Twitter that Naya will be found safe and sound !!" Lovato tweeted. "Come on all of you! Let's put this energy over there: they will find it healthy and alive !!"
