  Antiferromagnets have large potential for ultrafast coherent switching of
magnetic order with minimum heat dissipation. In novel materials such as
Mn$_2$Au and CuMnAs, electric rather than magnetic fields may control
antiferromagnetic order by N\'eel spin-orbit torques (NSOTs), which have,
however, not been observed on ultrafast time scales yet. Here, we excite
Mn$_2$Au thin films with phase-locked single-cycle terahertz electromagnetic
pulses and monitor the spin response with femtosecond magneto-optic probes. We
observe signals whose symmetry, dynamics, terahertz-field scaling and
dependence on sample structure are fully consistent with a uniform in-plane
antiferromagnetic magnon driven by field-like terahertz NSOTs with a torkance
of (150$\pm$50) cm$^2$/A s. At incident terahertz electric fields above 500
kV/cm, we find pronounced nonlinear dynamics with massive N\'eel-vector
deflections by as much as 30{\deg}. Our data are in excellent agreement with a
micromagnetic model which indicates that fully coherent N\'eel-vector switching
by 90{\deg} within 1 ps is within close reach.
