  Materials potentially hosting Kitaev spin-liquid states are considered
crucial for realizing topological quantum computing. However, the intricate
nature of spin interactions within these materials complicates the precise
measurement of low-energy spin excitations indicative of fractionalized
excitations. Using Na$_{2}$Co$_2$TeO$_{6}$ as an example, we study these
low-energy spin excitations using the time-resolved resonant elastic x-ray
scattering (tr-REXS). Our observations unveil remarkably slow spin dynamics at
the magnetic peak, whose recovery timescale is several nanoseconds. This
timescale aligns with the extrapolated spin gap of $\sim$ 1 $\mu$eV, obtained
by density matrix renormalization group (DMRG) simulations in the thermodynamic
limit. The consistency demonstrates the efficacy of tr-REXS in discerning
low-energy spin gaps inaccessible to conventional spectroscopic techniques.
