Albert Einstein didn't "figure out" E=mc² in a single moment. It was a result of his development of the theory of special relativity, which he published in 1905.

Here's a breakdown:

* 1905: Einstein published his paper "On the Electrodynamics of Moving Bodies," which laid out the foundations of special relativity. This theory showed that time and space are not absolute but relative to the observer's motion.

* 1905 (later in the year): As a consequence of his work on special relativity, Einstein derived the famous equation E=mc² in a separate paper titled "Does the Inertia of a Body Depend Upon Its Energy Content?" This equation demonstrated that mass and energy are equivalent and can be converted into one another.

So, while it's not a precise date, the year 1905 marks the year Einstein developed the theory of special relativity and subsequently derived the E=mc² equation.