A system and method for making an edge section of a thin, high purity fused silica glass sheet. The method includes a step of directing a laser to melt through the glass sheet with localized heating of a narrow portion of the glass sheet to form an edge section of the glass sheet, and continuing the edge section to form a closed loop defining a perimeter of the glass sheet. The method further includes rapidly cooling the glass sheet through the glass transition temperature as the melted glass of the edge section contracts and/or solidifies to form an unrefined-bullnose shape extending between first and second major surfaces of the glass sheet.