The challenging propagation environment, combined with the hardware limitations of mmWave systems, gives rise to the need for accurate initial access beam alignment strategies with low latency and high achievable beamforming gain. Much of the recent work in this area either focuses on one-sided beam alignment, or, joint beam alignment methods where both sides of the link perform a sequence of fixed channel probing steps. Codebook-based non-adaptive beam alignment schemes have the potential to allow multiple user equipment (UE) to perform initial access beam alignment in parallel whereas adaptive schemes are favourable in achievable beamforming gain. This work introduces a novel deep learning based joint beam alignment scheme that aims to combine the benefits of adaptive, codebook-free beam alignment at the UE side with the advantages of a codebook-sweep based scheme at the base station. The proposed end-to-end trainable scheme is compatible with current cellular standard signaling and can be readily integrated into the standard without requiring significant changes to it. Extensive simulations demonstrate superior performance of the proposed approach over purely codebook-based ones.