I have some cultural questions for you. In the United States, "bread" would normally mean bread only, with no "filling."
Bread filled with slices of meat, lettuce, cheese, etc would be a "sandwich." But when squeezed, the filling of a sandwich would not "burst" out. It might "fall out" if handled by a baby.
If you tell me that the filling "burst out," it suggests a sweet pastry with a jelly-like filling. "When the baby grabbed my jelly doughnut, the filling burst out."