Story highlights Two-year-old AJ Burgess was in kidney failure, and his father was a perfect match

The hospital originally denied the transplant due to the father's incarceration

The boy had surgery Wednesday, and his new kidney is already working

(CNN) Two-year-old AJ Burgess received a new kidney Wednesday after a prolonged battle with hospital officials who postponed his original October surgery when his father, a perfect donor match, violated his parole and was arrested.

"This is an unexpected Thanksgiving miracle," family attorney Muwali Davis said while the baby was in recovery at Children's Healthcare of Atlanta at Egleston. "To watch this child that no one expected to live, and now for him to have a chance at a healthy life, it's unbelievable.

"His parents and family are overwhelmed with gratitude," Davis added. "They want everyone to know that with faith, all things are possible. When the situation was very bleak, it was their faith and the support of the community that pulled them through this."

According to AJ's mother, Carmellia Burgess, the boy was born prematurely without working kidneys. On a GoFundMe page Burgess established, she says AJ's father, Anthony Dickerson, was "found to be a perfect match" and volunteered to donate one of his kidneys.

Emory Healthcare in Atlanta was set to remove Dickerson's kidney on October 3, according to Burgess, and soon after, AJ would undergo the transplant at Egleston.

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