  The transient Galactic black hole candidate MAXI J0637-430 went through an
outburst in 2019--20 for the very first time. This outburst was active for
almost 6 months from November 2019 to May 2020. We study the spectral
properties of this source during that outburst using archival data from NICER,
Swift, and NuSTAR satellites/instruments. We have analyzed the source during 6
epochs on which simultaneous NICER--NuSTAR and Swift/XRT--NuSTAR data were
available. Using both phenomenological and physical model fitting approaches,
we analyzed the spectral data in the broad $0.7-70$ keV energy band. We first
used a combination of disk blackbody with power-law, disk blackbody with broken
power-law, and disk blackbody with power-law and bmc models. For a better
understanding of the accretion picture, e.g., understanding how the accretion
rates change with the changing size of the perceived Compton cloud, we used the
two-component advective flow (TCAF) model with broken power-law, TCAF with
power-law and bmc models. For last 3 epochs, the diskbb+power-law and TCAF
models were able to spectrally fit the data for acceptable $\chi^2/DOF$.
However, for the first 3 epochs, we needed an additional component to fit
spectra for acceptable $\chi^2/DOF$. From our analysis, we reported about the
possible presence of another component during these first 3 epochs when the
source was in the high soft state. This additional component in this state is
best described by the bulk motion Comptonization phenomenon. From the TCAF
model fitting, we estimated the average mass of the source as
$8.1^{+1.3}_{-2.7}~M_\odot$.
