The Antennae galaxies are a spectacular example of a burst of star formation triggered by the encounter of two galaxies, being an ideal source to understand how the dynamics of galaxy mergers drives star formation. We present archive ALMA CO(3−2) and VLT near-IR H2 spectro-imaging observations, and new ALMA 13CO(2−1) and dust continuum observations, at ~50 pc resolution. Combining tracers of density and velocity structure of the gas and its energetics, we demonstrate that star formation involves a complex interplay of merger-driven gas dynamics and turbulence, and the dissipation of the gas kinetic energy. We focus on a compact, bright H2 source, associated with cold molecular gas and dust continuum emission, located where the velocity gradient in the interaction region is observed to be the largest. The characteristics of this source suggest that we are witnessing the formation, initiated by turbulent dissipation, of a cloud massive enough (~4×106M⊙) to form a super star cluster within 1 Myr.