Ava’s grief-stricken family, who have invited media to attend, requested people not to wear black to the funeral.
Mourners lit candles as they left the cathedral.
Ava’s coffin was brought there in a horse-drawn carriage.
Her family members carried her coffin, dressed with pictures of the 12-year-old, into the funeral.
They were followed by loved ones.
Photos show a long stream of well-wishers, dressed in bright attire, enter the cathedral for the emotional service, just two days before Christmas.
The Arch Bishop said: “There is little sadder in life that death of a child. Grief we are experiencing today is overwhelming so my deepest sympathy and that of Catholic community goes out to Ava’s family and her friends.
“Those memories will continue to live in your hearts. I’m told she would try anything… didn’t fear anything that’s good she won’t be afraid to step into the light of God.
“Some of you will remember her as a daredevil who always brightened up the day of those present.”
He went on to say Ava loved singing and dancing and going on holiday. He said: “She was very energetic and even famous on Tik Tok.
“Ava was loved by so many people undoubtedly heaven will be a happier place. No doubt she will be taken in by storm.”
Mourners also sang hymns at the service.
They were given copies of the order of service, which included pictures of Ava as a younger child.
Staff from Holy Trinity Catholic Primary School in Garston, Liverpool, where Ava attended, were seen at the funeral.
A 14-year-old boy, who cannot be named for legal reasons, has been charged with Ava’s murder and could face trial next year.