  The excitonic insulator is an electronically-driven phase of matter that
emerges upon the spontaneous formation and Bose condensation of excitons.
Detecting this exotic order in candidate materials is a subject of paramount
importance, as the size of the excitonic gap in the band structure establishes
the potential of this collective state for superfluid energy transport.
However, the identification of this phase in real solids is hindered by the
coexistence of a structural order parameter with the same symmetry as the
excitonic order. Only a few materials are currently believed to host a dominant
excitonic phase, Ta$_2$NiSe$_5$ being the most promising. Here, we test this
scenario by using an ultrashort laser pulse to quench the broken-symmetry phase
of this transition metal chalcogenide. Tracking the dynamics of the material's
electronic and crystal structure after light excitation reveals surprising
spectroscopic fingerprints that are only compatible with a primary order
parameter of phononic nature. We rationalize our findings through
state-of-the-art calculations, confirming that the structural order accounts
for most of the electronic gap opening. Not only do our results uncover the
long-sought mechanism driving the phase transition of Ta$_2$NiSe$_5$, but they
also conclusively rule out any substantial excitonic character in this
instability.
