  Determining the efficiency with which gas is converted into stars in galaxies
requires an accurate determination of the total reservoir of molecular gas
mass. However, despite being the most abundant molecule in the Universe, H$_2$
is challenging to detect through direct observations and indirect methods have
to be used to estimate the total molecular gas reservoir. These are often based
on scaling relations from tracers such as CO or dust, and are generally
calibrated in the Milky Way. Yet, evidence that these scaling relations are
environmentally dependent is growing. In particular, the commonly used
CO-to-H$_2$ conversion factor (X$_{\rm CO}$) is expected to be higher in
metal-poor and/or strongly UV-irradiated environments. We use new SOFIA/FIFI-LS
observations of far-infrared fine structure lines from the ionised and neutral
gas and the Meudon photodissociation region model to constrain the physical
properties and the structure of the gas in the massive star-forming region of
30 Doradus in the Large Magellanic Cloud, and determine the spatially resolved
distribution of the total reservoir of molecular gas in the proximity of the
young massive cluster R136. We compare this value with the molecular gas mass
inferred from ground-based CO observations and dust-based estimates to quantify
the impact of this extreme environment on commonly used tracers of the
molecular gas. We find that the strong radiation field combined with the
half-solar metallicity of the surrounding gas are responsible for a large
reservoir of "CO-dark" molecular gas, leaving a large fraction of the total
H$_2$ gas (> 75%) undetected when adopting a standard X$_{\rm CO}$ factor in
this massive star-forming region.
