Abstract Realization of topological superconductors (TSCs) hosting Majorana fermions is an exciting challenge in materials science. Majorana fermions are predicted to emerge at vortex cores of two-dimensional (2D) TSCs and at both ends of one-dimensional (1D) TSCs; these two types of TSCs have been explored independently in different materials. Here, a system which has a potential to access both 1D and 2D TSCs in a single platform, Pb(111)/Bi(111) heterostructure, is proposed. One to twenty bilayers (BLs) of Bi(111) ultra-thin films are epitaxially fabricated on TlBiSe$_2$, and an intriguing evolution of electronic states upon variation of Bi-layer thickness is revealed by angle-resolved photoemission spectroscopy. The metallic quantum-well states at 1–2BLs are found to turn into the Rashba states at 5–20BLs, via the semiconducting states at 3BL. Fabrication of a Pb(111) film on 20BL Bi(111) enables observation of the proximity-induced superconductivity in Bi(111) as evident from a 1 meV energy gap at 5 K; these energy and temperature scales are considerably larger than those of Rashba superconductors. The Pb/Bi heterostructure serves as a versatile platform to study the interplay among proximity-induced superconductivity, band structure, and topology.