The earliest credible evidence suggests that Ahmed al-Ghaffar in Yemen was among the first to drink coffee, in the middle of the 15th century.
While the precise individual who first ever drank coffee may be lost to history, the historical record points to Yemen as the origin of coffee consumption as we understand it today. Ahmed al-Ghaffar's accounts provide the earliest evidence of coffee seeds being roasted and brewed in a manner similar to modern coffee preparation. This is distinct from earlier potential uses of the coffee plant, which might have involved eating the cherries or using the leaves in different ways. The roasting and brewing process is what truly marks the beginning of coffee drinking as a beverage.
Therefore, while we cannot definitively name "the first" coffee drinker, Ahmed al-Ghaffar represents the earliest documented evidence of coffee consumption in the way we know it.