Thanks to its capability of acquiring full-view frames at multiple kilohertz, ultrafast ultrasound imaging unlocked the analysis of rapidly changing physical phenomena in the human body, with pioneering applications such as ultrasensitive flow imaging in the cardiovascular system or shear-wave elastography. The accuracy achievable with these motion estimation techniques is strongly contingent upon two contradictory requirements: a high quality of consecutive frames and a high frame rate. Indeed, the image quality can usually be improved by increasing the number of steered ultrafast acquisitions, but at the expense of a reduced frame rate and possible motion artifacts. To achieve accurate motion estimation at uncompromised frame rates and immune to motion artifacts, the proposed approach relies on single ultrafast acquisitions to reconstruct high-quality frames and on only two consecutive frames to obtain 2-D displacement estimates. To this end, we deployed a convolutional neural network-based image reconstruction method combined with a speckle tracking algorithm based on cross-correlation. Numerical and in vivo experiments, conducted in the context of plane-wave imaging, demonstrate that the proposed approach is capable of estimating displacements in regions where the presence of side lobe and grating lobe artifacts prevents any displacement estimation with a state-of-the-art technique that relies on conventional delay-and-sum beamforming. The proposed approach may therefore unlock the full potential of ultrafast ultrasound, in applications such as ultrasensitive cardiovascular motion and flow analysis or shear-wave elastography.