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The unprecedented angular resolution and sensitivity of ALMA makes it possible to unveil disk populations in distant ($>$2 kpc), embedded young cluster environments. We have conducted an observation towards the central region of the massive protocluster G286.21+0.16 at 1.3 mm. With a spatial resolution of 23 mas and a sensitivity of 15 $\rm μJy~beam^{-1}$, we detect a total of 38 protostellar disks. These disks have dust masses ranging from about 53 to 1825 $M_\oplus$, assuming a dust temperature of 20 K. This sample is not closely associated with previously identified dense cores, as would be expected for disks around Class 0 protostars. Thus, we expect our sample, being flux limited, to be mainly composed of Class I/flat-spectrum source disks, since these are typically more massive than Class II disks. Furthermore, we find that the distributions of disk masses and radii are statistically indistinguishable with those of the Class I/flat-spectrum objects in the Orion molecular cloud, indicating similar processes are operating in G286.21+0.16 to regulate disk formation and evolution. The cluster center appears to host a massive protostellar system composed of three sources within 1200 au, including a potential binary with 600 au projected separation. Relative to this center, there is no evidence for widespread mass segregation in the disk population. We do find a tentative trend of increasing disk radius versus distance from the cluster center, which may point to the influence of dynamical interactions being stronger in the central regions.