The family - including a young woman, a man in his late teens or early 20s and a child, possibly aged around 18 months - were last seen in Queens Park, Brighton on Wednesday 6 December.
Officers found a grey and white tent and travel cot in the park, sparking fears they are without shelter.
The female is described as 5ft tall and slim with blonde, messy hair and blue eyes. Police said she speaks with a northern accent.
The man has been described as slim and at least 6ft tall. He was last seen wearing a black tracksuit and a scarf-type covering over the lower part of his face, police said.
The toddler is believed to be a boy with pale skin, blonde hair and rosy cheeks. He was last seen wearing a thick red snowsuit and black or dark blue wellington boots.
Detective Superintendant Kris Ottery said: “The group are also believed to be in possession of a pushchair that is overladen with baggage.
“Specially-trained officers have been searching the park and other areas of interest, with the assistance of drones and the National Police Air Service helicopter, completing house-to-house enquiries, liaising with local transport networks and carrying out CCTV trawls in the vicinity.”
They have released photographs of the tent and cot as an appeal to any members of the public who may have seen these items in the area in the past couple of weeks.
Detective Superintendent Ottery added: “Our priority has always been to make sure the two people and toddler are safe and well.
“We appeal to the young man and woman subject of this search. If you believe you are the people we are seeking please make contact with us to let us know that you are safe and well.”
Anyone with information is asked to continue to report to police either online or by calling 101 quoting Operation Sorrel. Always dial 999 in an emergency.