The phrase "for the first/last etc. time" can be replaced with several synonyms depending on the context. For example, "maiden" can be used to describe the first time something is being done, such as a maiden voyage. "Inaugural" could also be used in this context. If something is happening for the last time, words like "final," "ultimate," or "culminating" would be appropriate. For a rare occurrence, synonyms like "exceptional" or "unprecedented" could be used. "Debut" could also be used for a first-time event, such as a debut album. It's important to select the appropriate synonym based on the context and desired tone of the sentence.