Strontium titanate [SrTiO3 (STO)], a perovskite oxide with an extremely high gate-tunable dielectric constant (ε) due to quantum paraelectric phases, is attracting considerable attention for yielding various physical phenomena when two-dimensional (2D) layers are integrated. Superconductivity is such a typical phenomenon. However, the influence of the STO substrates on enhancing transition temperatures (Tc) for (atomically) thin 2D flakes attached to them has been rarely investigated. Here, we report gate-tunable and gradual four-terminal resistance drops with critical onset T (TCR) and scanning tunneling spectroscopy (STS) spectra in devices comprising thin TaS2 flakes attached on monolayer hexagonal boron nitride (hBN) spacer/STO substrates. Observation of STS spectra confirms the presence of local superconducting gaps Δ (∼1.5 meV) with transition T (TΔC) three-times higher than previous reports of Tc under absent pressure and strong position dependence of Δ. Depending on Δ on back gate voltages (Vbg) and magnetic fields, there is a strong correlation between TCR and the onset Tc of superconductivity, implying an enhancement of approximately five times compared with the previous highest-onset Tc values without pressure as the applied Vbg increases. The high onset Tc and Δ are discussed based on screening of the long-range Coulomb interaction (CI) due to the high-ε of SrTiO3, while the short-ranged CI remains strong in the 2D limit, causing the superconductivity. Using a monolayer hBN/SrTiO3 substrate with Vbg opens doors to Tc enhancement in thin superconducting layers integrated on it and wide application due to the solid-state high-ε substrates.