Massive main-sequence stars have convective cores and radiative envelopes, but can also have sub-surface convection zones caused by partial ionisation zones. However, the convective properties of such regions strongly depend on opacity and therefore a star's metallicity. Non-rotating 1D evolution models of main-sequence stars between $7 M odot $ and metallicity of the Small Magellanic Cloud (SMC) galaxy suggest tenuous (if any) sub-surface convection zones when using the Rayleigh number as a criterion for convection owing to their substantially lower metallicity compared to Galactic massive stars. We test if massive stars of different metallicities both inside and outside of asteroseismically calibrated stability windows for sub-surface convection exhibit different properties in stochastic low-frequency (SLF) variability. Thus we aim to constrain the metallicity dependence of the physical mechanism responsible for SLF variability commonly found in light curves of massive stars. We extract customised light curves from the ongoing NASA Transiting Exoplanet Survey Satellite (TESS) mission for a sample of massive stars using an effective point spread function (ePSF) method, and compare their morphologies in terms of characteristic frequency, $ char $, and amplitude using a Gaussian process (GP) regression methodology. We demonstrate that the properties of SLF variability observed in time-series photometry of massive stars are generally consistent across the metallicity range from the Milky Way down to the SMC galaxy, for stars both inside and outside of the sub-surface stability windows based on the Rayleigh number as a criterion for convection. We conclude that non-rotating 1D stellar structure models of sub-surface convection cannot alone be used to explain the mechanism giving rise to SLF variability in light curves of massive stars. Additionally, the similar properties of SLF variability across a large range in metallicity, which follow the same trends in mass and age in the Hertzsprung--Russell (HR) diagram at both high and low metallicity, support a transition in the dominant mechanism causing SLF variability from younger to more evolved stars. Specifically, core-excited internal gravity waves (IGWs) are favoured for younger stars lacking sub-surface convection zones, especially at low-metallicity, and sub-surface convection zones are favoured for more evolved massive stars.