We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of the submillimeter dust continuum and H₂D⁺ 1₁₀-1₁₁ emission toward two evolved, potentially protostellar cores within the Ophiuchus molecular cloud, Oph A SM1 and SM1N. The data reveal small-scale condensations within both cores, with mass upper limits of M 0.02 M _☉ (~20 M _Jup). The SM1 condensation is consistent with a nearly symmetric Gaussian source with a width of only 37 AU. The SM1N condensation is elongated and extends 500 AU along its major axis. No evidence for substructure is seen in either source. A Jeans analysis indicates that these sources are unlikely to fragment, suggesting that both will form single stars. H₂D⁺ is only detected toward SM1N, offset from the continuum peak by ~150-200 AU. This offset may be due to either heating from an undetected, young, low-luminosity protostellar source or first hydrostatic core, or HD (and consequently H₂D⁺) depletion in the cold center of the condensation. We propose that SM1 is protostellar and that the condensation detected by ALMA is a warm (T ~ 30-50 K) accretion disk. The less concentrated emission of the SM1N condensation suggests that it is still starless, but we cannot rule out the presence of a low-luminosity source, perhaps surrounded by a pseudodisk. These data observationally reveal the earliest stages of the formation of circumstellar accretion regions and agree with theoretical predictions that disk formation can occur very early in the star formation process, coeval with or just after the formation of a first hydrostatic core or protostar.