Who were the first epistolary writers?
In addition to the wonderful post above...
The most influential epistolary writer who pre-dates those mentioned is St. Paul (Paul of Tarsus, 6 - 67 A.D.), whose letters founded and spread Christianity.
His letters include at least 13 "books" (some say 16) in the New Testament:
Epistle (Epistula) to the Romans; First Epistle to the Corinthians; Second Epistle to the Corinthians; Epistle to the Galations; Epistle to the Ephesians; Epistle to the Phillipians; Epistle to the Colossians; First Epistle to the Thesssolonians; Second Epistle to the Thessolonians; First Epistle to Timothy; Second Epistle to Timothy; Epistle to Titus; Epistle to Philemon.
Although these are rarely canonized individually as "literature," collectively they are irreplaceable. In fact, Michael H. Hart, in his book The 100 Most Influential Persons in History (1978), ranks St. Paul #6, the highest ranking Western "author" on the list. Enotes says:
Paul's influence on Christian thinking arguably has been more significant than any other New Testament author.
The first epistolary authors were Samuel Richardson (1689–1761), whose Pamela (1740) and Clarissa (1747–48) were extremely popular, and which established a taste for fiction. At the same time, Henry Fielding (1707–1754), after writing a brief epistolary novel, Shamela (1741), which was based satirically on Pamela, embarked on straightforward narratives, publishing Joseph Andrews (1742), Jonathan Wild (1743), Tom Jones (1749), and Amelia (1751). Ever since these writers wrote in this fashion, this genre of narrative fiction has flourished, and continues to flourish in our own day. Some of the most popular literature today is in the epistolary style, since the art of the letter adds such a personal and emotional touch.
The beginning of epistolary fiction is known to date from the publication of the first epistolary novel Pamela, or Virtue Rewarded by Samuel Richardson in 1740. This novel had a great success particularly among women. It was followed by Clarissa in 1748. But, since your question addresses "writing" in general , you might cite epistolary autobiographies such as Turkish Letters by Lady Mary Wortley Montagu, and published in 1763 right after her death.