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We report on results of our upgraded Giant Metrewave Radio Telescope (uGMRT) observations for an early-stage merging galaxy cluster, CIZA J1358.9-4750 (CIZA1359), in Band-3 (300--500 MHz). We achieved the image dynamic range of $\sim 38,000$ using the direction dependent calibration and found a candidate of diffuse radio emission at 4~$σ_{rms}$ significance. The flux density of the candidate at 400~MHz, $24.04 \pm 2.48$~mJy, is significantly positive compared to noise, where its radio power, $2.40 \times 10^{24}$~W~Hz$^{-1}$, is consistent with those of typical diffuse radio sources of galaxy clusters. The candidate is associated with a part of the X-ray shock front at which the Mach number reaches its maximum value of $\mathcal{M}\sim 1.7$. The spectral index ($F_ν\propto ν^α$) of the candidate, $α= - 1.22 \pm 0.33$, is in agreement with an expected value derived from the standard diffusive shock acceleration (DSA) model. But such a low Mach number with a short acceleration time would require seed cosmic-rays supplied from active galactic nucleus (AGN) activities of member galaxies, as suggested in some other clusters. Indeed, we found seven AGN candidates inside the diffuse source candidate. Assuming the energy equipartition between magnetic fields and cosmic-rays, the magnetic field strength of the candidate was estimated to be $2.1~μ$G. We also find head-tail galaxies and radio phoenixes or fossils near the CIZA1359.