We consider a nonminimal quartic inflation scenario in the minimal ({U\left(1\right)}{X}) extension of the Standard Model (SM) with the classical conformal invariance, where the inflaton is identified with the ({U\left(1\right)}{X}) Higgs field ((\varphi )). By virtue of the classically conformal invariance and the radiative ({U\left(1\right)}{X}) symmetry breaking via the Coleman-Weinberg mechanism, the inflationary predictions (in particular, the tensor-to-scaler ratio (r)), the ({U\left(1\right)}{X}) coupling ({g}{X}), and the ({U\left(1\right)}{X}) gauge boson mass ({m}{{Z}^{\prime }}) are all determined by only two free parameters: the inflaton mass ({m}{\varphi }) and its mixing angle (\theta ) with the SM Higgs field. FASER can search for a long-lived scalar, which is the inflaton in our scenario, for the parameter ranges (0.1\lesssim {m}{\varphi }\left[\mathrm{GeV}\right]\lesssim 4) and ({10}^{-5}\lesssim \theta \lesssim {10}^{-3}). Therefore, if such a scalar is discovered at FASER, both ({m}{\varphi }) and (\theta ) would be fixed, leading to the predictions for (r), ({g}{X}), and ({m}{{Z}^{\prime }}) in our model. These predictions can be tested by future cosmological observations and LHC searches for the ({Z}^{\prime }) boson resonance.