Superconducting radio frequency (SRF) cavities which are made from bulk niobium and operated at cryogenic temperatures around 2 K, are essential components in modern particle accelerators. Due to the sustainability issues related to niobium, which is considered a critical metal, and the huge power consumption of accelerator facilities, the community has discussed alternative high(er)-temperature superconductors for many years. Recent advances in Nb₃Sn thin film technology have revitalized this discussion. In particular, the ability to coat copper with high-quality Nb₃Sn surface layers has sparked hope that we can finally move beyond conventional niobium technology. We have demonstrated that a specific magnetron co-sputtering process enables the synthesis of fully superconducting Nb₃Sn, even at low temperatures, where copper diffusion can be disregarded. When coating sapphire substrates, we achieve critical temperatures (Tc) of 17.9 K. The same process (i.e. without post-annealing) on copper yields Tc values of around 15 K and lower critical fields of approximately 200 mT at 4 K. Moving beyond flat substrates, we coated a higher order mode (HOM) antenna — a three-dimensional, mushroom-like object — with Nb₃Sn, achieving similar Tc values at all positions on its surface. We anticipate that, by 2030, Nb₃Sn-coated copper cavities will surpass the quality factor of standard Nb bulk cavities.