Police Scotland previously carried out an investigation into Sophia's death, alongside other fatalities at the hospital campus including leukaemia patient Milly Main, 10, who died after a catheter became infected when she was in remission.
Last year, Lord Advocate Dorothy Bain KC said the circumstances of Sophia's death gave rise to "significant public concern" to justify a fatal accident inquiry (FAI).
Sophia Smith was just 11 days old when she died at the Royal Hospital for Children at the Queen Elizabeth University Hospital (QEUH) campus on 11 April 2017.
"We are pleased that a fatal accident inquiry has been finally set up and hope that by the end of this process we will know the truth about our daughter and why her life was so tragically and heartbreakingly cut short.
The inquiry got under way at Glasgow Sheriff Court on Monday, with Sophia's parents seeking answers as to why their daughter died.
