Quiz Answer
First, let dispense with the obvious: In answer to the question you posed, the U. S. Mint's first commemorative coin was the emission of 1848 Philadelphia quarter eaglescounterstamped CAL. in January of the following year to denote that they were coined from gold of the new California mines.

For more information, see NGC Coin Explorer:
LIBERTY HEAD $2.50 1848 "CAL." $2.5 MS(https://www.ngccoin.com/coin-explorer/liberty-head-250-1840-1907-pscid-57/1848-cal.-2.5-ms-coinid-17749)

Recovering from my recent surgeries gave me a lot of down time at home, and it was inevitable that I'd run out of current magazines and newsletters to read. Fortunately, Ihave many books that were purchased years ago and quickly shelved for another day. One of these is a two-volume oral history anthology titled San Francisco Memoirs,compiled and introduced by Malcolm E. Barker. In Volume Two, which covers the post-Gold Rush years 1852-99, I found a really interesting account of a traveler's experienceswith money in and around San Francisco in 1869-70. William Fraser Rae published this account in 1871 within his own book, Westward by Rail: The New Route to the East, whichwas evidently intended for his British readers.

There are several points of specific interest in this account. It's already well documented that paper money was shunned in California, yet it was available more in SanFrancisco as a curiosity than as a routine medium of exchange. It's possible that it may have been useful for discreetly mailing money to others, and fractional currency noteswere used in this manner for many years after their discontinuance. It also confirms that nothing smaller than a dime was in general circulation in California. The writerevidently didn't know that a "bit" had indeed been an actual coin, the Spanish one real piece, and it still survived as a unit of value even after the coins ceasedcirculating.

There is also confirmation of what many in Congress considered to be a fantasy concocted by Western silver interests to justify adoption of a 20-cent piece in 1875. Severalyears prior to that date there was clear evidence that the absence of a circulating five-cent piece was a problem, though one that most were content to ignore. While half dimeshad been coined at the San Francisco Mint regularly since 1863, few were in circulation, and this may be explained by the fact that jewelers bought them up for fashioning intocharms, buttons and pendants.

Mark Twain famously wrote of the disdain he was shown by a miner upon offering a half dime as payment of some small sum, so there seems to have been two schools of thoughtregarding its usefulness in western commerce. Finally, the routine usage of double eagles in circulation helps to explain why so many, particularly San Francisco Mint coins of the1850s-70s, are found obviously worn.