We present the first search for z >= 7, continuum-confirmed Lyman break sources with NIRISS/WFS spectroscopy over the Abell 2744 Frontier Fields cluster, as part of the GLASS-JWST-ERS survey. With similar to 15 hr of preimaging and multiangle grism exposures in the F115W, F150W, and F200W filters, we describe the general data handling (i.e., reduction, cleaning, modeling, and extraction processes) and analysis for the GLASS-JWST survey. We showcase the power of JWST to peer deep into reionization, when most intergalactic hydrogen is neutral, by confirming two galaxies at z = 8.04 +/- 0.15 and z = 7.90 +/- 0.13 by means of their Lyman breaks. Fainter continuum spectra are observed in both the F150W and F200W bands, indicative of blue (-1.69 and -1.33) UV slopes and moderately bright absolute magnitudes (-20.37 and -19.68 mag). We do not detect strong Ly alpha in either galaxy, but do observe tentative (similar to 2.7-3.8 sigma) He ii lambda 1640 angstrom, O iii]lambda lambda 1661,1666 angstrom, and N iii]lambda lambda 1747,1749 angstrom line emission in one, suggestive of low-metallicity, star-forming systems with possible nonthermal contributions. These novel observations provide a first look at the extraordinary potential of JWST/NIRISS for confirming representative samples of bright z >= 7 sources in the absence of strong emission lines, and gain unprecedented insight into their contributions toward cosmic reionization.