The “twins embedding” technique presented in Boone et al. 2020 is able to standardize the absolute magnitudes of Type Ia supernovae (SNe Ia) to within 0.084 magnitudes, given a well-calibrated spectrum of each supernova within 5 rest-frame days of maximum brightness. The question then arises: can this remarkable precision be obtained using a single spectrum away from maximum brightness? We present an answer to this question via an extension of the twins embedding technique, using a deep multi-layer perceptron, a simple type of artificial neural network, to accurately predict the phase, extinction parameter, and embedding coordinate of an SN Ia from any single photometrically calibrated spectrum from -10 to +40 rest-frame days after maximum brightness. Using the same Gaussian process regression model presented in Boone et al. 2020, we are then able to use these predicted embeddings to calibrate the maximum brightness of a given SN Ia with comparably excellent precision (adding in quadrature an error of <0.025 mag). These results indicate that it is possible to obtain distance modulus estimates using just a single spectrum, observed anywhere from -10 to +40 days beyond maximum brightness, with dramatically better precision than light curve-based techniques that require multiple observations. This work can be immediately applied to planning studies of nearby supernova peculiar velocities using existing instruments, as well as high-redshift supernova surveys with spectroscopy, as on the Roman Space Telescope. We also present a second neural network model that can produce an estimate of the spectral energy distribution of an SN Ia given its phase, color, and twins embedding coordinate. This model enables forward-modeling fits to any mix of spectra and broadband photometry, and also makes possible highly representative simulations of spectra and light curves for survey design.