We present the first results from a detailed spectral-timing analysis of a long ( \sim 130 ks ) XMM-Newton observation and quasi-simultaneous NuSTAR and Swift observations of the highly-accreting narrow-line Seyfert 1 galaxy Mrk 1044 . The broadband ( 0.3 - 50 keV ) spectrum reveals the presence of a strong soft X-ray excess emission below \sim 1.5 keV , iron K _ { \alpha } emission complex at \sim 6 - 7 keV and a ‘ Compton hump ’ at \sim 15 - 30 keV . We find that the relativistic reflection from a high-density accretion disc with a broken power-law emissivity profile can simultaneously explain the soft X-ray excess , highly ionized broad iron line and the Compton hump . At low frequencies ( [ 2 - 6 ] \times 10 ^ { -5 } Hz ) , the power-law continuum dominated 1.5 - 5 keV band lags behind the reflection dominated 0.3 - 1 keV band , which is explained with a combination of propagation fluctuation and Comptonization processes , while at higher frequencies ( [ 1 - 2 ] \times 10 ^ { -4 } Hz ) , we detect a soft lag which is interpreted as a signature of X-ray reverberation from the accretion disc . The fractional root-mean-squared ( rms ) variability of the source decreases with energy and is well described by two variable components : a less variable relativistic disc reflection and a more variable direct coronal emission . Our combined spectral-timing analyses suggest that the observed broadband X-ray variability of Mrk 1044 is mainly driven by variations in the location or geometry of the optically thin , hot corona .