When looking for synonyms for the phrase "presented itself," there are a variety of options to choose from. For instance, one could say that an opportunity or situation "arose," "appeared," "manifested," "happened," or "turned up." Alternatively, one could use terms like "exposed," "revealed," or "unveiled" to describe the emergence of an idea, concept, or solution. In addition, phrases like "came to light," "came into view," or "came forward" could be used to express a similar idea. Ultimately, the choice of synonym will depend on the context in which it is being used and the specific connotations that the writer or speaker wishes to convey.