Beam alignment - finding optimal analog beamforming (BF) weights - is a critical bottleneck for millimeter wave ( mmWave) systems. Existing beam alignment approaches typically assume that devices adopt codebooks of analog beams with uniform coverage, from which a good beam pair is selected after an exhaustive search or sweeping a few candidate beams. In this work, we propose a beam alignment method that is grid-less - the analog beam is synthesized from the continuous set instead of being chosen from a quantized codebook, and one-shot - nearoptimal BF weights are directly predicted without searching even a small number of candidates. With unsupervised training, the proposed method uses a few learned probing beams to sense the channel and predict the BF weights. Our experiments show that it can get within 0.32 dB of the hard theoretical upper bound, outperforms the exhaustive search in terms of the signal-to- noise ratio (SNR), reduces the beam sweeping latency by over 20x, while scaling optimally to multiple DEs and fitting within the 5G NR beam alignment framework.