Sure, it’s perfectly possible.
If you have all the data used during the training (including random seeds, initial values, learning rates, elements used on each batch and so on…), the whole information relevant to repeat the process and functionally equivalent hardware, you can replicate the process and obtain the exact same system.
You can try for yourself, but it’s quite obvious: we are not talking about quantum computing, thus each step of the process is strictly deterministic and reproducible if you don’t throw away relevant data (such as, for example, the values provided by random sources during the process).