In this work, we develop an inflationary scenario in which Tsallis holographic dark energy (THDE) provides an effective inflaton potential driving early-universe inflation within $f(R,T)$ gravity. Throughout this work, $\rho_{\rm THDE}$ is interpreted as a generalized holographic vacuum energy density operative during the inflationary epoch and mapped to an effective single-field description, $V_{\rm eff}(\phi)\equiv\rho_{\rm THDE}$, rather than being treated as a late-time dark-energy component. Adopting the Granda-Oliveros infrared cutoff, we derive the slow-roll relations and delineate a viable region of the parameter space $(\alpha,\beta,\delta,\lambda)$ consistent with the Planck-ACT low-band combined likelihood (P-ACT-LB) from ACT DR6. Exploiting the parametric dependence of the THDE density on the Hubble expansion rate, we reconstruct the effective inflaton potential $V(\phi)$ across the observable window. We show that both the inflaton field excursion and the potential gradient $|V'|/(V M_p)$ are predominantly controlled by the matter-geometry coupling $\lambda$. In particular, moderately large values $\lambda \gtrsim \mathcal{O}(10^{2})$ tend to suppress the field excursion below the Planck scale while ensuring $|V'|/(V M_p) \gtrsim \mathcal{O}(1)$, consistent with the distance conjecture and the refined de~Sitter swampland bound. We further investigate the reheating phase following inflation. In addition to the primordial nucleosynthesis requirement $T_{\rm BBN} \simeq 4\,\mathrm{MeV}$, the observational bound $\Delta N_{\rm eff} \le 0.17$ imposes an additional lower limit on the reheating temperature through the integrated contribution of primordial gravitational waves (PGWs). During stiff reheating stages with $\omega_{\rm re} > 1/3$, the high-frequency PGW spectrum is significantly enhanced, potentially leading to observable signatures in the frequency bands of forthcoming gravitational-wave detectors. For suitable parameter values, the resulting PGW signal may enter the projected sensitivity range of upcoming experiments. Overall, this work presents a unified and observationally consistent realization of holographic inflation in $f(R,T)$ gravity, jointly constrained by CMB observations, reheating dynamics, primordial gravitational waves, and swampland bounds.
