It generally takes about 5-7 years to progress to Director. Promotion is based on performance in the current role and future potential.
Given the current growth of Aldi, there is opportunity to progress. However I would expect that this process would be similar to that when applying - you have to be exceptional at what you do and be willing to work hard.
As expected it is not easy to progress. It is subjective to the leader's perception. There can be a lack of transparency relating to performance indicators for promotion.