On the basis of various data such as ALMA, JVLA, Chandra, {\it Herschel}, and
{\it Spitzer}, we confirmed that two protostellar candidates in Oph-A are bona
fide protostars or proto-brown dwarfs (proto-BDs) in extremely early
evolutionary stages. Both objects are barely visible across infrared (IR, i.e.,
near-IR to far-IR) bands. The physical nature of the cores is very similar to
that expected in first hydrostatic cores (FHSCs), objects theoretically
predicted in the evolutionary phase prior to stellar core formation with gas
densities of $\sim$ 10$^{11-12}$ cm$^{-3}$. This suggests that the evolutionary
stage is close to the FHSC formation phase. The two objects are associated with
faint X-ray sources, suggesting that they are in very early phase of stellar
core formation with magnetic activity. In addition, we found the CO outflow
components around both sources which may originate from the young outflows
driven by these sources. The masses of these objects are calculated to be $\sim
0.01-0.03$ $M_\odot$ from the dust continuum emission. Their physical
properties are consistent with that expected from the numerical model of
forming brown dwarfs. These facts (the X-ray detection, CO outflow association,
and FHSC-like spectral energy distributions) strongly indicate that the two
objects are proto-BDs or will be in the very early phase of protostars which
will evolve more massive protostars if they gain enough mass from the
surroundings. The ages of these two objects are likely to be within $\sim 10^3$
years after the protostellar core (or second core) formation, taking into
account the outflow dynamical times ($\lesssim$ 500 yrs).