Investigating Protostellar Accretion is a Cycle 1 JWST program using the NIRSpec+MIRI integral field units to obtain 2.9-28 mu m spectral cubes of five young protostars with luminosities of 0.2-10,000 L-circle dot in their primary accretion phase. This paper introduces the NIRSpec 2.9-5.3 mu m data of the inner 840-9000 au with spatial resolutions from 28 to 300 au. The spectra show rising continuum emission; deep ice absorption; emission from H-2, H i, and [Fe ii]; and the CO fundamental series in emission and absorption. Maps of the continuum emission show scattered light cavities for all five protostars. In the cavities, collimated jets are detected in [Fe ii] for the four <320 L-circle dot protostars, two of which are additionally traced in Br alpha. Knots of [Fe ii] emission are detected toward the most luminous protostar, and knots of [Fe ii] emission with dynamical times of <30 yr are found in the jets of the others. While only one jet is traced in H-2, knots of H-2 and CO are detected in the jets of four protostars. H-2 is seen extending through the cavities, showing that they are filled by warm molecular gas. Bright H-2 emission is seen along the walls of a single cavity, while in three cavities narrow shells of H-2 emission are found, one of which has an [Fe ii] knot at its apex. These data show cavities containing collimated jets traced in atomic/ionic gas surrounded by warm molecular gas in a wide-angle wind and/or gas accelerated by bow shocks in the jets.