We report Atacama Large Millimeter/submillimeter Array and Very Large Array 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 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 0.5-1.2 M-circle dot 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 similar to 300 to similar to 1400 yr. 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 freefall times of similar to 100 yr, or whether they are evolving on Kelvin-Helmholtz times of several thousand years. The number of these sources imply a lifetime of similar to 6000 yr, in closer agreement with the Kelvin-Helmholtz time. In this case, rotational and/or magnetic support could be slowing the collapse.