At the time that is a phrase commonly used to indicate a particular point in time when an event occurred. However, there are a number of synonyms that can be used to replace this phrase in order to add variation and create a different tone in writing. Some possible alternatives include: during, when, while, as, at the moment that, at the point when, amidst, and amidst the time that. Each of these phrases can have a slightly different connotation, so it is important to consider the context in which they are used in order to choose the most appropriate option.