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Why does the viscosity of molten glass increase so sharply as it cools?

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The sharp increase in the viscosity of molten glass as it cools is primarily due to the steep temperature dependence of the molecular response time.1

As a liquid cools toward the glass transition temperature ( $T_{g}$ ), the time required for molecules to rearrange themselves increases significantly. When the temperature drops below $T_{g}$ , this response time becomes much larger than experimentally accessible time scales. Consequently, the liquidlike mobility disappears, and the atomic configuration becomes effectively frozen into fixed positions.1

While some sources describe this state as an undercooled liquid, it is more accurate to note that as the material cools through the glass transformation range, its viscosity rises enormously—often exceeding $10^{18}$ poise—until the substance behaves as a rigid amorphous solid. This transition is not marked by an abrupt volume change, as seen in crystallization, but rather by this dramatic, continuous increase in resistance to flow as molecular motion is restricted.213