Lee Parker, 33, repeatedly struck baby Aya's head against a bathroom door and wall in a fit of temper after drinking heavily on Christmas Eve and taking drugs.
Parker was told he would serve at least 15 years and two months' imprisonment after previously admitting murder.
Mr Justice Phillips said Parker had carried out a "sustained and murderous attack".
"On Christmas Eve at about 9pm a tragic and dark change occurred in your behaviour, no doubt because you were drinking heavily and had used cocaine and cannabis," he said.
"That initial bout of violence broke Aya's jaw but it is not clear how you did that. At about 1am, you carried out further attacks of extreme violence smashing her head against the bathroom door and wall.
"Aya suffered catastrophic head injuries, including skull fractures in several places. Such severe injuries are rarely seen in a child as young as Aya. She could not have survived for long."
The judge added: "You have never provided an explanation as to why you carried out these terrible things to your own child.
"The only explanation for the extreme and violent attack is that you had lost your temper having drunk heavily and had taken cocaine and cannabis.
"The result is the tragic loss of a very young and innocent life."
Bristol Crown Court heard he alerted the emergency services at 1am on Christmas Day - a short time after he had killed Aya.
Her mother Zofia Kucharczyk had left Parker - who she regarded as a caring and loving father - looking after their daughter while she went out for the night with her new partner and his parents.
Miss Kucharczyk planned to return to the flat in Kingswood, South Gloucestershire, on Christmas morning, with Parker leaving to spend the rest of the day with a friend in Melksham, Wiltshire.
The court heard Aya may have been unsettled because she was teething and Parker attacked her after drinking two bottles of wine and a third of a bottle of vodka.
He never provided an explanation and police pieced together what may have happened from forensic and medical evidence.
A post-mortem examination found Aya had suffered an injury to her jaw between two and four hours before she died.
Two hours later, Aya sustained fatal blunt force trauma injuries to the head after being hit against the bathroom door and wall.
Parker, of Britton Gardens, Kingswood, pleaded guilty to a charge of murder on the day he was due to stand trial.
The defendant and Miss Kucharczyk had met online in September 2015 and she fell pregnant almost immediately. Aya was born the following June.
They decided they did not wish to be a couple but would share a two-bedroom flat in Kingswood to bring up Aya together.
Dean Armstrong QC, defending, said Parker wished to look after his daughter financially and be a "proper father".
"It is certainly the case that he cannot offer an explanation and has no memory of what happened that night," he said.
"He accepts he had been drinking and he accepts by his plea that he was responsible for the death of his daughter. He has never tried to deflect the blame onto anybody else."
Detective Chief Inspector Gary Haskins, from Avon and Somerset Police, said: "As Aya's father, Lee Parker was expected to love and protect her at all costs.
"Instead, for reasons we will never know, he robbed her of the life which lay ahead of her and caused unimaginable pain to those who loved her.
"The death of any baby is always a tragedy but the circumstances of this case make it particularly emotive.
"Aya was just six months old and was about to enjoy her first Christmas, yet because of the actions of her father it was sadly her last."