Optical switches offer several benefits over electronics switches, including better scalability, lower power consumption, and lower latency. However, their implementation faces several challenges, including electronic transceivers to be able to support sub-nanosecond clock and data recovery time. This is required to efficiently handle data center traffic that is dominated by small data packets. Recent research shows that, scalable and sub-nanosecond data recovery can be achieved by synchronizing the clocks of all end-points connected to an optical switch in frequency and phase. In such a system, thermallyinduced change of propagation time through standard single mode fiber (SMF-28) necessitates the clock phases to be tracked due to variations in the data centers temperature. Hollow core fiber has been shown to have a thermal coefficient of delay 20 times smaller than SMF-28, offering potential to simplify the clock phase tracking and to increase the distance scale of data center networks. In this paper, we show how the low thermal coefficient of delay in hollow core fiber enables sub-nanosecond optical switching system with only initial frequency and phase synchronization. We obtained error-free real-time transmission of 60 ns packets over 1 km clock and 1 km hollow core data fiber with under 625 ps clock recovery time in both a point-to-point and a 2-to-1 optically switched 25.6 Gb/s real-time system. Based on our results, we estimate that sub-nanosecond clock recovery can be achieved for a 100 m size data center cluster interconnected by an optical switch using hollow core fiber, frequency synchronization and only a single phase calibration at the start-up.