Dangerous weather hampered the search for the infant on Tuesday, in waters off South Australia's southeast coast.
Emergency services are scouring the Port MacDonnell area off the state's Limestone Coast after making a shocking discovery on Monday.
They had earlier been alerted to an abandoned car that was left with its engine running near Cape Northumberland about 11.15am on Monday.
The bodies of a 36-year-old mother from Compton, a small community near Mount Gambier, and a girl aged under three were found in the ocean soon afterwards and retrieved with assistance from local fishermen.
SA Police Commissioner Grant Stevens said he had not had any direct feedback on how the fishermen were coping.
"But I'm sure we can all put themselves put ourselves in their shoes - it would be heartbreaking and very difficult," he said.
Police had spoken to the husband of the woman, who was the father of the children, Mr Stevens said.
The search was being conducted on the belief that the missing boy had fallen from the cliff.
"Despite the weather today, which is not good, searching is continuing for the infant (but) there are no indications at this point of any specific location to search," Mr Stevens said.
"Searching for a small child and recovering a woman and a child from the water will take its toll on people who are involved in that search exercise, and they are genuinely committed to finding this young child as quickly as possible."
Earlier, police said there was "no information to suggest that any other persons are involved in the incident and reports will be prepared for the coroner''.
SA Premier Peter Malinauskas said there were a lot of unanswered questions, making it very difficult to understand exactly what had transpired.
"These types of tragedies are the ones that shock you to the core," he said on Tuesday.
"If it involves children, that breaks your heart, particularly when we know there is currently a two-month-old baby that is missing, and that's hard to get your head around.
"I think we can hope and pray for the best in this instance, and that's certainly what we're doing at the moment."Â
Detectives and specialist forensic officers are at the scene of the search off Cape Northumberland, the state's southernmost point.
Local mayor Kylie Boston said such tragedies were ''always difficult for smaller communities''.
''Everyone's just a little bit shocked at the moment," Southern Limestone Coast Council's Ms Boston told AAP.
"We'll let the police do the work they need to do, and everyone will just continue to support everyone."
She paid tribute to the "fabulous" volunteers amid rough weather that was affecting the search.
"I was just at the boat ramp before, it's very windy and quite choppy, which is not helping them," she said.
Anyone who saw the woman's car, a white 2015 Isuzu MUX with SA Registration S592 BJR, or has any dashcam footage should contact police.
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