Screening　promising　hydrogen　evolution　reaction　(HER)　electrocatalysts　for　water　splitting　is　crucial　for　the　industrial　scalability　of　sustainable　energy　storage.　As　HER　catalysts,　two-dimensional　(2D)　MXenes　are　promising　substitution　materials　for　platinum.　Tuning　the　surface　termination　and　loading　a　single　atom　can　help　to　improve　the　electrocatalytic　performance　of　2D　MXenes.　We　utilized　density　functional　theory　(DFT)　calculations　to　explore　the　catalyst　activity,　thermal　stability,　and　dynamic　stability　of　2D　single　atom-loaded　MXenes　with　surface　terminations.　We　demonstrate　that　21　uninvestigated　2D　single-atom　MXene　catalysts,　among　264　promising　candidates,　show　an　electrocatalytic　activity　surpassing　that　of　platinum.　Among　the　21　most　promising　HER　catalysts,　7　(Ti3C2I2-Ir,　Ti3C2Br2-Cu,　Ti3C2Br2-Pt,　Ti3C2Cl2-Cu,　Ti3C2Cl2-Pt,　Ti3C2Se2-Au,　and　Ti3C2Te2-Nb)　are　dynamically　and　thermally　stable.　Furthermore,　machine　learning　tools　predicted　the　catalyst　activity　and　thermal　stability　using　elemental　properties　that　are　easily　available　in　chemical　data　repositories.