Superconductivity in TiSe2 emerges when the charge density wave (CDW) order is suppressed under pressure or doping. Recent theoretical and experimental studies suggest that a Lifshitz transition plays a key role in stabilizing the superconducting phase. Here, we present muon spin resonance measurements of pressurized TiSe2, revealing a two-gap superconducting state. Our results indicate that the smaller gap contributes unexpectedly strongly to the total superfluid density. This effect is consistent with an enhanced density of states in a newly formed Fermi surface pocket at the Lifshitz transition. These findings provide microscopic insight into the interplay between CDW suppression, Fermi surface reconstruction, and multi-gap superconductivity in TiSe2, demonstrating how pressure-induced changes in electronic structure can shape superconducting properties in layered materials.