Investigating Protostellar Accretion is a Cycle 1 JWST program using the NIRSpec+MIRI integral field units to obtain 2.9–28 μm spectral cubes of five young protostars with luminosities of 0.2–10,000 L⊙ in their primary accretion phase. This paper introduces the NIRSpec 2.9–5.3 μm 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 H2, 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⊙ protostars, two of which are additionally traced in Brα. 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 H2, knots of H2 and CO are detected in the jets of four protostars. H2 is seen extending through the cavities, showing that they are filled by warm molecular gas. Bright H2 emission is seen along the walls of a single cavity, while in three cavities narrow shells of H2 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.