The unidentified child has become known as "Baby Grace" and authorities are still trying to find out her identity.
Her body was found by a fisherman inside a blue plastic utility box that washed ashore along the Intercoastal Waterway
Authorities say forensic dental examination has narrowed the girl's age to between 2 and 3 years. She is described as white, 32 to 35 inches tall and 25 to 30 pounds. She had waist-long, wavy blond or light brown hair. She was wearing a Target-brand pink, flowing skirt, a pink or red shirt and white light-up tennis shoes with purple flowers on them.
"Someone is missing a child," said Dr. Stephen Pustilnik, the Galveston County chief medical examiner. "A grandparent who hasn't seen their grandchild in the last couple of weeks, a playmate who's missing their playmate and hasn't seen him for a while, there's an aunt, there's an uncle someplace, maybe locally, maybe around the state, maybe somewhere around the nation."
The case is bringing grown cops to tears and has captured the hearts of hard-core investigators who are determined to solve the mystery, CBS' The Early Show co-anchor Hannah Storm reports.
"This is an emotional case for us. Anyway you look at it, cases like this are incredibly emotional," Maj. Ray Tuttoilmondo of the Galveston County Sheriff's Office.
Residents held a memorial service Sunday to help focus attention on the case.
Attendees gathered around a 4-foot-tall wooden cross bearing the words "In loving Memory of Baby Grace."
After speeches, prayers, songs and poems, attendees took the cross by boat to the small uninhabited island where the child's body was found.
Some people have raised the possibility that the child's body may be that of Madeleine McCann, the 4-year-old British girl whose disappearance from a resort hotel in Portugal in May has made international headlines.
Tuttoilmondo said that was unlikely.
"We are in contact with authorities in Portugal to absolutely rule it out, but we are very, very confident at this point that it's not going to be Madeleine," Tuttoilmondo said.
Local authorities and the FBI are going through missing person reports from across country in an effort to identify the girl.
Galveston County Crime Stoppers set up a memorial fund to pay for her funeral as well as an account to offer a reward for anyone who helps to solve this crime.
The Galveston County Medical Examiner's Office ruled the child had been dead for at least two weeks and sustained a skull fracture. The cause of death has not been determined but authorities are treating the case as a homicide.
Anyone with information is asked to call the Galveston County sheriff's Office at 409-766-2222, the agency's tip line at 866-248-8477 or any Crime Stoppers organization.