Khalil al Shami, 34, was digging through the wreckage of his brother’s building in the Syrian city of Jinderes on Monday when he saw his sister-in-law’s legs and a baby girl still attached to her by the umbilical cord. She had given birth while trapped under the debris.

Mr. Shami said in an interview that he cut the dust-covered umbilical cord and the baby let out a cry. He said he kept digging and digging, thinking that the mother was still alive, too. His sister-in-law did not survive, but his niece is safely in a hospital.

“The mother was supposed to give birth the next day, but it looks as if she was delivered in shock,” said Mr. Shami.

In another Syrian city, a video shows two small girls sandwiched under the rubble, one lying on top of the other, as a man tries to dig them out. He asks them, “Do you know how to play?” and one of the little girls cries, “No, no, get me out.”

A teenage boy wearing a red shirt covered in dust filmed himself under the twisted metal and brick that remained of his home. He said he did not know how to describe what he was feeling, not knowing if he would live or die. Then a scream is heard on the video.

More than two, three families are stuck, you hear their screams and our neighbors. God help us,” the boy said in the video.

Many families, having fled their homes in subfreezing weather, wearing only their night clothes, are taking shelter in cars or public spaces like mosques and schools.

For the children of Syria, the earthquake comes after 12 years of accumulated suffering from war, poverty and multiple displacements as families fled the conflict.

“It is trauma on trauma, it is heartbreak on heartbreak,” said Mr. English from UNICEF. “It’s a long road ahead to recovery.”

The UN’s immediate focus is on ensuring that affected children and families have access to safe drinking water and sanitation services — critical in preventing illness in the early days of a crisis — and feeding kits. UNICEF is also gearing up to provide psychological aid.