We present the first results from a detailed analysis of a new, long ($sim100$ ks) XMM-Newton observation of the narrow-line Seyfert 1 galaxy PG 1404$+$226 which showed a large-amplitude, rapid X-ray variability by a factor of $sim7$ in $sim10$ ks with an exponential rise and a sharp fall in the count rate. We investigate the origin of the soft X-ray excess emission and rapid X-ray variability in the source through time-resolved spectroscopy and fractional root-mean-squared (rms) spectral modeling. The strong soft X-ray excess below 1 keV observed both in the time-averaged and time-resolved spectra is described by the intrinsic disk Comptonization model as well as the relativistic reflection model where the emission is intensive merely in the inner regions ($r_{rm in}<1.7 r_{rm g}$) of an ionized accretion disk. We detected no significant UV variability while the soft X-ray excess flux varies together with the primary power-law emission (as $F_{{rm primary}}propto F_{{rm excess}}^{1.54}$), although with a smaller amplitude, as expected in the reflection scenario. The observed X-ray fractional rms spectrum is approximately constant with a drop at $sim0.6$ keV and is described by a non-variable emission line component with the observed energy of $sim0.6$ keV and two variable spectral components: a more variable primary power-law emission and a less variable soft excess emission. Our results suggest the `lamppost geometry for the primary X-ray emitting hot corona which illuminates the innermost accretion disk due to strong gravity and gives rise to the soft X-ray excess emission.