Bulk FeSe is superconducting with a critical temperature T_c ≅ 8 K and SrTiO₃ is insulating in nature, yet high-temperature superconductivity has been reported at the interface between a single-layer FeSe and SrTiO₃. Angle-resolved photoemission spectroscopy and scanning tunneling microscopy measurements observe a gap opening at the Fermi surface below ≈60 K. Elucidating the microscopic properties and understanding the pairing mechanism of single-layer FeSe is of utmost importance as it is a basic building block of iron-based superconductors. Here, we use the low-energy muon spin rotation/relaxation technique to detect and quantify the supercarrier density and determine the gap symmetry in FeSe grown on SrTiO₃ (100). Measurements in applied field show a temperature-dependent broadening of the field distribution below ~60 K, reflecting the superconducting transition and formation of a vortex state. Zero-field measurements rule out the presence of magnetism of static or fluctuating origin. From the inhomogeneous field distribution, we determine an effective sheet supercarrier density n_s^2D ≅ 6×10¹⁴ cm^–2 at T → 0 K, which is a factor of 4 larger than expected from ARPES measurements of the excess electron count per Fe of 1 monolayer FeSe. The temperature dependence of the superfluid density n_s(T) can be well described down to ~10 K by simple s-wave BCS, indicating a rather clean superconducting phase with a gap of 10.2(1.1) meV. The result is a clear indication of the gradual formation of a two-dimensional vortex lattice existing over the entire large FeSe/STO interface and provides unambiguous evidence for robust superconductivity below 60 K in ultrathin FeSe.