This paper investigates the effectiveness of multipath-decorrelating antenna motion in reducing the initialization time of global navigation satellite system (GNSS) receivers employing low-cost single-frequency antennas for carrier-phase differential GNSS (CDGNSS) positioning. Fast initialization times with low-cost antennas will encourage the expansion of CDGNSS into the mass market, bringing the benefits of globally referenced centimeter-accurate positioning to many consumer applications, such as augmented reality and autonomous vehicles, that have so far been hampered by the several-meter-level errors of traditional GNSS positioning. Poor multipath suppression common to low-cost antennas results in large and strongly time-correlated phase errors when a receiver is static. Such errors can result in the CDGNSS initialization time, the so-called time to ambiguity resolution (TAR), extending to hundreds of seconds—many times longer than for higher cost survey-grade antennas, which have substantially better multipath suppression. This paper demonstrates that TAR can be significantly reduced through antenna motion, particularly gentle wavelength-scale random antenna motion. Such motion acts to decrease the correlation time of the multipath-induced phase errors. A priori knowledge of the motion profile is shown to further reduce TAR, with the reduction shown to be more pronounced as the initialization scenario is more challenging.