Kevin Eves allegedly caused multiple fractures to eight-week-old Harper Denton in the weeks before she collapsed at their family home last year.
A post-mortem examination of the baby girl identified 34 rib fractures, 11 classic metaphyseal fractures or lesions, two fractured metatarsal bones, one in each foot, and a skull fracture, London's Old Bailey heard.
There was also bruising, mostly beneath the scalp and the skin of the face, and damage around Harper's mouth, the court was told.
Prosecuting, Sally Howes QC said Eves had met the child's mother, Cherinea Denton, via the internet, two years before Harper was born.
Shortly after 6am on 12 June last year, she said Ms Denton called 999 and told the operator: “My baby’s not breathing. Her dad's just brought her down and said she's not breathing."
Although Harper was rushed to hospital where she was pronounced dead less than an hour later.
Bleeding was found in the retinas of both eyes, inflicted at least 48 hours before Harper's death, the court heard.
She was also found to to have injuries that were three weeks old.
“These injuries, and the time period during which they were inflicted, tell the tale of a totally dependent, vulnerable, helpless baby girl who was subjected to a catalogue of escalating violence which only came to an end with her untimely death,” Ms Howes said.
“It is the Crown's case that the person responsible for the injuries inflicted upon, and ultimately, the death of Harper is Kevin Eves, her own father.”
Eves, formerly known as Forbes, moved in with Ms Denton in 2016, the court heard.
Ms Denton was aware that the trainee plumber had a previous conviction from 2006 when he was sentenced to nine years in jail, Ms Howes said.
He allegedly told Ms Denton that the conviction was due to a fight at a house party, when it was actually for another offence, the prosecutor added.
By the time of Harper’s birth, their relationship had broken down and they lived separate lives, she said.
Eves has denied the charges of murder and grievous bodily with intent.
The trial continues.
Agencies contributed to this report