Superconductivity (SC) is one of the most intriguing physical phenomena in nature. Nucleation of SC has long been considered highly unfavorable if not impossible near ferromagnetism, in low dimensionality and, above all, out of non-superconductor. Here we report observation of SC with TC near 4 K in Ni/Bi bilayers that defies all known paradigms of superconductivity, where neither ferromagnetic Ni film nor rhombohedra Bi film is superconducting in isolation. This highly unusual SC is independent of the growth order (Ni/Bi or Bi/Ni), but highly sensitive to the constituent layer thicknesses. Most importantly, the SC, distinctively non-s pairing, is triggered from, but does not occur at, the Bi/Ni interface. Using point contact Andreev reflection, we show evidences that the unique SC, naturally compatible with magnetism, is triplet p-wave pairing. This new revelation may lead to unconventional avenues to explore novel SC for applications in superconducting spintronics.