  Exploring the nature of exotic multiquark candidates such as the $X(3872)$
plays a pivotal role in understanding quantum chromodynamics (QCD). Despite
significant efforts, consensus on their internal structures is still lacking.
As a prime example, it remains a pressing open question to decipher the
$X(3872)$ state between two popular exotic configurations: a loose hadronic
molecule or a compact tetraquark. We demonstrate a novel approach to help
address this problem by studying the $X(3872)$ production in heavy ion
collisions, where a hot fireball with ample light as well as charm
(anti-)quarks is available for producing the exotics. Adopting a multiphase
transport model (AMPT) for describing such collisions and implementing
appropriate production mechanism of either molecule or tetraquark picture, we
compute and compare a series of observables for $X(3872)$ in Pb-Pb collisions
at the Large Hadron Collider. We find the fireball volume plays a crucial role,
leading to a 2-order-of-magnitude difference in the $X(3872)$ yield and a
markedly different centrality dependence between hadronic molecules and compact
tetraquarks, thus offering a unique opportunity for distinguishing the two
scenarios. We also make the first prediction of $X(3872)$ elliptic flow
coefficient to be tested by future experimental measurements.
