It's not necessarily the correct answer, but I quickly found the following, gleaned from the bi-annual Official Register of the United States. Prior to the 1870s, only officers and salaried personnel were recorded. Beginning in 1873, all employees were recorded:

Elizabeth Wyer was a memorandum clerk at the San Francisco Mint in 1865, earning an annual salary of $1,872. She was born in Ireland, apparently circa 1833. She appeared in the 1862 San Francisco directory as a widow and worked as a “Confectionary,” and was a memorandum clerk according to the 1864 directory.

In the 1870s, there were a number of female Mint employees working in the coining room as coiners and adjusters. In 1871, several female adjusters earned an annual salary of $1,092 in Philadelphia. In 1873, adjusters at Philadelphia earned $1.75 per day, while those in San Francisco earned $1,260 annually.

According to the Mint "Timeline." two women were hired as adjusters on October 10, 1795. I don't know their names. My study of Mint employees ends with 1793.

1. These women were not just the first women hired as employees of the Mint, but the first women employed anywhere in the Federal Government.

2. Martin Summers was a night watchman at the Mint from 1793 until his death in 1804. He did not have a wife or daughter named Rachel.

3. The women were mentioned in an article in The Numismatist in May, 2010, by Walt Ostromecki. The article says they both left Mint employment in 1801.