The observed indications {for} a new scalar resonance with a mass around 95\,GeV, initially reported by LEP and supported by CMS and ATLAS in di-photon, $\tau \tau$, and $W^+ W^-$ channels, motivate exploring its discovery potential at future electron-positron colliders. This study focuses on the production of the new scalar ($S$) {via} $e^+ e^- \rightarrow ZS $ with $Z \rightarrow \mu^+ \mu^- $ and $S \rightarrow b \bar{b}$ and optimizes the signal recognition using the recoil-mass method. By employing deep neural networks for signal-background discrimination, we demonstrate that a 95\,GeV scalar, mixing with the Standard Model Higgs by an angle of $\sim$0.1, can be observed with a 5$\sigma$ significance at $\sqrt{s}$ = 250\,GeV {or} 200\,GeV with 5~ab$^{-1}$ of integrated luminosity.