Carrier phase observations enable millimeter-level GNSS positioning, but their continuity is frequently disrupted by signal blockages and cycle slips. This limitation is particularly critical for low-cost and smartphone receivers, where weak antennas, urban multipath, and duty cycling cause frequent phase gaps that prevent reliable ambiguity resolution. Before addressing the full complexity of mass-market observations, the prediction methodology must be validated under controlled conditions. In this work we investigate whether machine learning, supported by precise satellite orbits and clocks, can predict carrier phase observations during signal gaps with millimeter-level accuracy. Twenty-four hours of Galileo data from the TORI permanent station (SPIN3 network, Torino, Italy) are processed at 30 s sampling using GFZ final SP3 and CLK products. After forming the ionosphere-free combination, an iterative carrier-phase based estimator removes the receiver clock, tropospheric delay, and ambiguity, reducing the residuals to a median standard deviation of 60 mm. Synthetic gaps from 60 s to 1800 s are introduced (1045 gaps total) and four prediction strategies are compared: polynomial fitting (degrees 3 and 5), Fourier-augmented polynomial, Gradient Boosting Regression with satellite geometry features, and Gaussian Process Regression. The Gradient Boosting model achieves the best overall performance, reaching 4.4 mm RMS for 60 s gaps, 9.4 mm for 5 min gaps, and 21 mm for 30 min gaps, well below the half-wavelength threshold required for cycle slip repair. These results demonstrate that geometry-aware gap prediction is feasible at the sub-wavelength level, providing a validated foundation for extending the approach to low-cost and smartphone GNSS receivers.