Transformers have become central to recent advances in audio classification. However, training an audio spectrogram transformer, e.g. AST, from scratch can be resource and time-intensive. Furthermore, the complexity of transformers heavily depends on the input audio spectrogram size. In this work, we aim to optimize AST training by linking to the resolution in the time-axis. We introduce multi-phase training of audio spectrogram transformers by connecting the seminal idea of coarse-to-fine with transformer models. To achieve this, we propose a set of methods for temporal compression. By employing one of these methods, the transformer model learns from lower-resolution (coarse) data in the initial phases, and then is fine-tuned with high-resolution data later in a curriculum learning strategy. Experimental results demonstrate that the proposed training mechanism for AST leads to improved (or on-par) performance with faster convergence, i.e. requiring fewer computational resources and less time. This approach is also generalizable to other AST-based methods regardless of their learning paradigms.