In　superconducting/ferromagnet　heterostructures,　spin-triplet　Cooper　pairs　that　carry　spin　information　are　crucial　for　the　realization　of　superconducting　spintronics.　It　has　been　theoretically　proposed　that　they　can　be　generated　and　controlled　by　the　magnetic　proximity　effect　and　spin-orbit　coupling　(SOC),　resulting　in　a　change　in　the　critical　temperature　(T　(C)).　However,　experiments　are　still　lacking,　which　limits　the　development　of　device　applications.　Here,　we　fabricate　a　series　of　Co/Nb/Pt　heterostructures　and　reference　samples,　where　the　SOC　and　magnetic　proximity　can　be　independently　controlled.　We　found　the　suppression　of　T　(C)　up　to　11%　by　the　different　Rashba-SOC　at　the　Nb/Pt　and　Nb/Cu　interfaces,　and　the　normalized　T　(C)/T　(C)　(0)　was　successfully　tuned　by　24%　with　the　coeffect　of　SOC　and　magnetic　proximity.　Through　rigorous　comparison,　we　attribute　the　tuning　of　superconductivity　to　the　spin-triplet　Cooper　pairs,　which　is　controlled　by　both　the　SOC　strength　and　magnetic　proximity.　Our　results　offer　a　new　pathway　to　control　superconductivity　with　SOC　and　pave　a　new　direction　for　the　design　of　superconducting　spintronics　devices.