## 2 Materials and Methods  
A single crystalline, stoichiometric sample of Sn\({}_{2}\)P\({}_{2}\)Se\({}_{6}\) was grown by chemical vapor transport [20] and subsequently cut to create a large 5 mm \(\times\) 5 mm face with a surface normal of [1 3.1 \(-\)3], which is 0.8\({}^{\circ}\) from the [1 3 \(-\)3] direction. In this work all Miller indices refer to the monoclinic space group in its standard setting \(Pc\), with lattice parameters \(a=6.81\) A, \(b=7.72\) A, \(c=11.70\) A and \(\beta=124.5^{\circ}\) at room temperature [7]. To characterize the equilibrium incommensurate modulation, we performed X-ray diffraction measurements at the Materials Science beamline of the Swiss Light Source (PSI, Villigen, Switzerland), using 7.0 keV X-rays with an energy resolution better than \(10^{-3}\)\(\Delta E/E\)[21]. The \((2D+2S)\) surface diffractometer was equipped with a Pilatus 100K 2-D detector [22]. The sample temperature was controlled using a cryogenic nitrogen blower. The relative intensities of superlattice reflections were obtained by subtracting the contribution of the Bragg reflection. For that, a second-order polynomial was fitted to the sufficient data points on both sides of the superlattice peak and used to interpolate the background intensity below the superlattice peak. To characterize the dynamics of the incommensurate modulation we performed pump-probe measurements with 400 nm pump excitation and X-ray diffraction as a probe. These were performed both at the microXAS beamline at the Swiss Light Source [23] and at end station No. 3 of the SACLA X-ray free-electron laser [24; 25; 26]. The measurements at SACLA had a higher time resolution of approximately 100 fs. Here we show only the time-resolved measurements from the Swiss Light Source since most of the dynamics is resolved with the lower time resolution and the general signal-to-noise ratio is better. At the Swiss Light Source, 7 keV X-ray pulses with a duration of 70 ps, corresponding to the size of an electron bunch, were vertically focused to less than 10 microns. The angle of incidence was set between 0.4 and 1.3 degrees, resulting in a 1/e penetration depth of the electric field ranging from 71 to 455 nm, calculated based on tabulated values from Ref. [27]. The long transverse structural coherence of the sample justifies the use of the field (rather than intensity) penetration depth because interference can take place over the entire probe volume. Pump pulses (400 nm, 100 fs (FWHM)) were generated by frequency doubling the output of an amplified femtosecond Ti:Sapphire laser using a commercial type-I BBO crystal. The pump photon energy of 3.1 eV exceeds the 1.76 eV bandgap [15; 28; 29]. \(p\)-polarized pump pulses were focused to a 400 \(\times\) 600 micron spot (FWHM) on the sample with an incidence angle of 13\({}^{\circ}\). Under these conditions the pump had a 1/e penetration depth in intensity of 20 nm, based on the absorption coefficient derived from ellipsometry measurements (see Supplementary Information), which is consistent with the results of [PERSON] and [PERSON] [29]. The laser was synchronized to the synchrotron and the repetition rate was reduced to 100 Hz to grant the system sufficient time to return to equilibrium, as the recovery time was found to be approximately 10 ms. The sample was cooled to a set temperature of 175 K using a cryogenic nitrogen blower and the X-ray diffracted intensity was measured using an avalanche photodiode. Since the superlattice reflections are in the vicinity of a more intense, commensurate Bragg reflection (Figure 1), there is some static background that does not vanish when crossing the phase transition. This background was determined from rotation scans, interpolated to the superlattice peak position and subtracted in the traces of the time-resolved diffraction data. Phonon band velocities were calculated _ab initio_ using density functional theory within the PBE-GGA [30] as implemented in Quantum Espresso [31; 32], with optimized norm-conserving Vanderbilt pseudopotentials [33].