Understanding cognitive processes in the brain demands sophisticated models capable of replicating neural dynamics at large scales. We present a physiologically inspired speech recognition architecture, compatible and scalable with deep learning frameworks, and demonstrate that end-to-end gradient descent training leads to the emergence of neural oscillations in the central spiking neural network. Significant cross-frequency couplings, indicative of these oscillations, are measured within and across network layers during speech processing, whereas no such interactions are observed when handling background noise inputs. Furthermore, our findings highlight the crucial inhibitory role of feedback mechanisms, such as spike frequency adaptation and recurrent connections, in regulating and synchronising neural activity to improve recognition performance. Overall, on top of developing our understanding of synchronisation phenomena notably observed in the human auditory pathway, our architecture exhibits dynamic and efficient information processing, with relevance to neuromorphic technology.