The silver BMW 218D was parked in the street, with the mother of the child leaving the vehicle for a few minutes and returning to find it gone.
Shortly afterwards, the car was seen being driven back to where it had been parked and a male youth was seen making off from the vehicle while the child was left safe in the back.
The youth is described as being white, of slim build and around 5ft 9ins and between 17 and 20-years-old. He was wearing a dark top with the hood up and dark bottoms.
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Inspector Jim Mutter said: “Fortunately the child was not harmed but this was an extremely upsetting experience for the mother and our enquiries are ongoing to trace the youth who was seen driving and exiting the car.
“We are asking anyone in the area at the time to check private CCTV and dash-cam to see if they have captured anything that could assist us.
“We are also particularly keen to speak to two older women who were sitting on a bench nearby as they may have vital information that could assist with our enquiries.”
Anyone who can help is asked to call Police Scotland on 101, quoting incident number 2136 of Tuesday, 31 December, 2024.