Observations of high-redshift galaxies provide a critical direct test to the theories of early galaxy formation, yet to date, only three have been spectroscopically confirmed at z > 12. Due to strong gravitational lensing over a wide area, the galaxy cluster field A2744 is ideal for searching for the earliest galaxies. Here we present JWST/NIRSpec observations of two galaxies: a robust detection at z_spec=12.393_-0.001^+0.004 , and a plausible candidate at z_spec=13.079_-0.001^+0.013 . The galaxies are discovered in JWST/NIRCam imaging and their distances are inferred with JWST/NIRSpec spectroscopy, all from the JWST Cycle 1 UNCOVER Treasury survey. Detailed stellar population modeling using JWST NIRCam and NIRSpec data corroborates the primeval characteristics of these galaxies: low mass (~10^8 M_⊙), young, rapidly assembling, metal-poor, and star-forming. Interestingly, both galaxies are spatially resolved, having lensing-corrected rest-UV effective radii on the order of 300-400 pc, which are notably larger than other spectroscopically confirmed systems at similar redshifts. The observed dynamic range of z ≳ 10 sizes spans over 1 order of magnitude, implying a significant scatter in the size-mass relation at early times. Deep into the epoch of reionization, these discoveries elucidate the emergence of the first galaxies.