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On July 13, 2022, NASA released to the whole world the data obtained by the James Webb Space Telescope (JWST) Early Release Observations (ERO). These are the first set of science-grade data from this long-awaited facility, marking the beginning of a new era in astronomy. In the study of the early universe, JWST will allow us to push far beyond z ~ 11, the redshift boundary previously imposed by the 1.7 um red cut-off of the Hubble Space Telescope (HST). In contrast, JWST's NIRCam reaches 5 um. Among the JWST ERO targets there is a nearby galaxy cluster SMACS 0723-73, which is a massive cluster and has been long recognized as a potential "cosmic telescope" in amplifying background galaxies. The ERO six-band NIRCam observations on this target have covered an additional flanking field not boosted by gravitational lensing, which also sees far beyond HST. Here we report the result from our search of candidate objects at z > 11 using these ERO data. In total, there are 87 such objects identified by using the standard "dropout" technique. These objects are all detected in multiple bands and therefore cannot be spurious. For most of them, their multi-band colors are inconsistent with known types of contaminants. If the detected dropout signature is interpreted as the expected Lyman-break, it implies that these objects are at z ~ 11--20. The large number of such candidate objects at such high redshifts is not expected from the previously favored predictions and demands further investigations. JWST spectroscopy on such objects will be critical.