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We report ALMA and VLA continuum observations that potentially identify the four youngest protostars in the Orion Molecular Clouds taken as part of the Orion VANDAM program. These are distinguished by bright, extended, irregular emission at 0.87 mm and 8 mm and are optically thick at 0.87 mm. These structures are distinct from the disk or point-like morphologies seen toward the other Orion protostars. The 0.87 mm emission implies temperatures of 41-170 K, requiring internal heating. The bright 8 mm emission implies masses of 0.5 to 1.2 M_sun assuming standard dust opacity models. One source has a Class 0 companion, while another exhibits substructure indicating a companion-candidate. Three compact outflows are detected, two of which may be driven by companions, with dynamical times of ~300 to ~400 years. The slowest outflow may be driven by a first hydrostatic core. These protostars appear to trace an early phase when the centers of collapsing fragments become optically thick to their own radiation and compression raises the gas temperature. This phase is thought to accompany the formation of hydrostatic cores. A key question is whether these structures are evolving on free fall times of ~100 years, or whether they are evolving on Kelvin-Helmholtz times of several thousand years. The number of these sources imply a lifetime of ~6000 years, in closer agreement with the Kelvin-Helmholtz time. In this case, rotational and/or magnetic support could be slowing the collapse.