Upgrades to the JUNO neutrino physics experiment are planned that will allow it to determine the neutrino mass hierarchy after six years of operations (of course, in addition, it will take time to build the upgrades to the experiment and get it running, so the real time frame for a definitive five sigma result is more like 2027, although less definitive results will be available long before then).
Other lines of evidence, most notably cosmological observations, already strongly favor a "normal" neutrino hierarchy in which neutrinos associated with tau leptons are more massive than neutrinos associated with muons which are in turn more massive than neutrinos associated with electrons.
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