No, Rome was not the first republic. Although it is one of the most famous examples of a republic in history, the concept of a republic predates Rome. The Roman Republic was established in 509 BC after the overthrow of the last Roman king, Tarquin the Proud, and it lasted until 27 BC when it transitioned into the Roman Empire.
Before Rome, various city-states in ancient Greece, such as Athens, practiced forms of self-governance that could be considered republics. Athens, for instance, developed an early form of democracy where citizens participated directly in decision-making processes. While the structures and systems varied significantly, these early forms of governance laid the groundwork for what we now recognize as republican principles.
Therefore, while Rome had a significant impact on the development of republicanism and its political ideas influenced many future nations, it was not the first to embody the concept of a republic.