  The tiny droplets of Quark Gluon Plasma (QGP) created in high-energy nuclear
collisions experience fast expansion and cooling with a lifetime of a few
$\text{fm}/c$. Despite the information provided by probes such as jet quenching
and quarkonium suppression, and the excellent description by hydrodynamical
models, direct access to the time evolution of the system remains elusive. We
point out that the study of hadronically-decaying $W$ bosons, notably in events
with a top-antitop quark pair, can provide key novel insight, into the time
structure of the QGP. This is because of a unique feature, namely a time delay
between the moment of the collision and that when the $W$-boson decay products
start interacting with the medium. Furthermore, the length of the time delay
can be constrained by selecting specific reconstructed top-quark momenta.
