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The first hydrostatic core, the first quasi-hydrostatic object formed during the star formation process, is still the observational missing link between the prestellar and protostellar phases, mainly due to its short lifetime. Although we have not established a clear method to identify this rare object, recent theoretical studies predict that the first core has millimeter continuum emission and low-velocity outflow with a wide opening angle. An extensive continuum/outflow survey toward a large number of $"$starless$"$ cores in nearby star-forming regions works as a pathfinder. We observed 32 prestellar cores in Taurus with an average density of $\gtrsim$10$^5$ cm$^{-3}$ in 1.3 mm continuum and molecular lines using the Atacama Large Millimeter/submillimeter Array$-$Atacama Compact Array (ALMA$-$ACA) stand-alone mode. Among the targets, MC35-mm centered at one of the densest $"$starless$"$ cores in Taurus has blueshifted/redshifted wings in the $^{12}$CO (2-1) line, indicating that there is deeply embedded object driving molecular outflow. The observed velocities and sizes of the possible outflow lobes are 2-4 km s$^{-1}$, and $\sim$2 $\times$10$^3$ au, respectively, and the dynamical time is calculated to be $\sim$10$^3$ yr. In addition to this, the core is one of the strongest N$_2$D$^{+}$ (3-2) emitters in our sample. All of the observed signatures do not conflict with any of the theoretical predictions about the first hydrostatic core so far, and thus MC35-mm is unique as the only first-core candidate in the Taurus molecular cloud.