  The high-redshift intergalactic medium (IGM) and the primeval galaxy
population are rapidly becoming the new frontier of extra-galactic astronomy.
We investigate the IGM properties and their connection to galaxies at
$z\geq5.5$ under different assumptions for the ionizing photon escape and the
nature of dark matter, employing our novel THESAN radiation-hydrodynamical
simulation suite, designed to provide a comprehensive picture of the emergence
of galaxies in a full reionization context. Our simulations have realistic
`late' reionization histories, match available constraints on global IGM
properties and reproduce the recently-observed rapid evolution of the mean free
path of ionizing photons. We additionally examine high-z Lyman-$\alpha$
transmission. The optical depth evolution is consistent with data, and its
distribution suggests an even-later reionization than simulated, although with
a strong sensitivity to the source model. We show that the effects of these two
unknowns can be disentangled by characterising the spectral shape and
separation of Lyman-$\alpha$ transmission regions, opening up the possibility
to observationally constrain both. For the first time in simulations, THESAN
reproduces the modulation of the Lyman-$\alpha$ flux as a function of galaxy
distance, demonstrating the power of coupling a realistic galaxy formation
model with proper radiation-hydrodynamics. We find this feature to be extremely
sensitive on the timing of reionization, while being relatively insensitive to
the source model. Overall, THESAN produces a realistic IGM and galaxy
population, providing a robust framework for future analysis of the high-z
Universe.
