Hybrid glasses are a novel class of glass formers that possess unique coordination bonds. Size effects on vitrification have been observed in other glassy materials such as metallic glasses and polymers, but their impact on hybrid glasses has yet to be explored. In this study, we examine the size-dependent vitrification behavior of hybrid glasses using fast scanning calorimetry across a broad range of heating and cooling rates. Our results are similar to that observed in polymer and metallic glasses, the glass transition temperature (Tg) is not significantly influenced by sample size at the micro-meter scale at cooling rates larger than or equal to 30 K/s. Furthermore, the vitrification enthalpy displays a clear dependence on sample size, with smaller samples exhibiting a larger overshoot enthalpy, which is attributed to a reduction of fictive temperature values (Tf) with size. These features originate from the network structure and flexibility of coordination bonding. Our findings suggest that the vitrification enthalpy is more fundamental than the temperature in size effects and that the low enthalpy state of smaller hybrid glass samples has implications for their functional properties.