Interest in the superconducting proximity effect has recently been reignited by theoretical predictions that it could be used to achieve topological superconductivity. Low-T$_{c}$ superconductors have predominantly been used in this effort, but small energy scales of ~1 meV have hindered the characterization of the emergent electronic phase, limiting it to extremely low temperatures. In this work, we use molecular beam epitaxy to grow topological insulator Bi$_{2}$Te$_{3}$ in a range of thicknesses on top of a high-T$_{c}$ superconductor Fe(Te,Se). Using scanning tunneling microscopy and spectroscopy, we detect {Delta}$_{ind}$ as high as ~3.5 meV, which is the largest reported gap induced by proximity to an s-wave superconductor to-date. We find that {Delta}$_{ind}$ decays with Bi$_{2}$Te$_{3}$ thickness, but remains finite even after the topological surface states had been formed. Finally, by imaging the scattering and interference of surface state electrons, we provide a microscopic visualization of the fully gaped Bi$_{2}$Te$_{3}$ surface state due to Cooper pairing. Our results establish Fe-based high-T$_{c}$ superconductors as a promising new platform for realizing high-T$_{c}$ topological superconductivity.
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