  The cosmological recombination radiation (CRR) is one of the guaranteed
spectral distortion signals from the early Universe. The CRR photons from
hydrogen and helium pre-date the last scattering process and as such allow
probing physical phenomena in the pre-recombination era. Here we compute the
modifications to the CRR caused by early dark energy models and varying
fundamental constants. These new physics examples have seen increased recent
activity in connection with the Hubble tension, motivating the exploratory
study presented here. The associated CRR responses are spectrally-rich but the
level of the signals is small. We forecast the possible sensitivity of future
spectrometers to these effects. Our estimates demonstrate that the CRR directly
depends to changes in the expansion history and recombination physics during
the pre-recombination era. However, futuristic sensitivities are required for
spectrometer-only constraints that are competitive with other cosmological
probes. Nevertheless, measurements of the CRR can directly reach into phases
that otherwise remain inaccessible, highlighting the potential these types of
observations could have as a probe of the early Universe. A combination with
${\it Planck}$ data further shows that a synergistic approach is very
promising.
