The UNCOVER Survey: First Release of Ultradeep JWST/NIRSpec PRISM spectra for ~700 galaxies from z~0.3-13 in Abell 2744

We present the design and observations of low resolution JWST/NIRSpec PRISM spectroscopy from the Ultradeep NIRSpec and NIRCam ObserVations before the Epoch of Reionization (UNCOVER) Cycle 1 JWST Treasury program. Targets are selected using JWST/NIRCam photometry from UNCOVER and other programs, and cover a wide range of categories and redshifts to ensure the legacy value of the survey. These categories include the first galaxies at $z\gtrsim10$, faint galaxies during the Epoch of Reionization ($z\sim6-8$), high redshift AGN ($z\gtrsim6$), Population III star candidates, distant quiescent and dusty galaxies ($1\lesssim z \lesssim 6$), and filler galaxies sampling redshift--color--magnitude space from $z\sim 0.1-13$. Seven NIRSpec MSA masks across the extended Abell 2744 cluster were observed, along with NIRCam parallel imaging in 8 filters (F090W, F115W, F150W, F200W, F277W, F356W, F410M, F444W, F480M) over a total area of ~26 arcmin$^2$, overlapping existing HST coverage from programs including the Hubble Frontier Fields and BUFFALO. We successfully observed 553 objects down to $m_{\mathrm{F444W}}\sim30\mathrm{AB}$, and by leveraging mask overlaps, we reach total on-target exposure times ranging from 2.4-16.7h. We demonstrate the success rate and distribution of confirmed redshifts, and also highlight the rich information revealed by these ultradeep spectra for a subset of our targets. An updated lens model of Abell 2744 is also presented, including 14 additional spectroscopic redshifts and finding a total cluster mass of $M_{\mathrm{SL}}=(2.1\pm0.3)\times10^{15}\,\mathrm{M}_{\odot}$. We publicly release reduced 1D and 2D spectra for all objects observed in Summer 2023 along with a spectroscopic redshift catalog and the updated lens model of the cluster (https://jwst-uncover.github.io/DR4.html).