Were there minted coins in the time of Mattan Torah

The obvious answer is yes, because of Medrashim that refer to various coinages in the time of the avos, and the halacha that Pidyon of Maaser sheini can only be done with minted coins, Kesef Tzura.

-בבא מציעא (מז ע"ב):  "רבי ישמעאל מאי היא – דתניא: (דברים יד) וצרת הכסף בידך – לרבות כל דבר הנצרר ביד, דברי רבי ישמעאל. רבי עקיבא אומר: לרבות כל דבר שיש עליו צורה".

-מעשר שני (פ"א מ"ב): "אין מחללין מעשר שני על אסימון ולא על המטבע שאינו יוצא ולא על המעות שאינן ברשותו".

-מאירי (ב"מ מז ע"ב): "מעשר שני אין מחללין אותו על אסימון אלא בכסף מפותח או בצורה או בכתב ואם פדה באסימון לא עשה כלום שנאמר: וצרת הכסף – כסף שיש עליו צורה. והאסימון הוא כסף שאינו טבוע לא בצורה ולא בכתב ונקרא בלשון תלמוד פולסא ואע"פ שבמסכת שבת פרק במה אשה אמרו אי משום צורתא ליבעי פולסא לא שתהא צורה בפולסא אלא פירוש הדברים ליבעי פולסא שיעשה בה צורה ויש מפרשים שיש בו צורה שוקעת כמו שביארנו במשנה".

This is inconsistent with the archeological record, which indicates that the minting of coins only began at the earliest eight hundred years before the common era. No coins have been found that predate that time, not in China, not in Europe, not in the Middle East.  Matan Torah was around 1300 BCE.

So I found it interesting to see this comment from Reb Yisrael Isserl of Ponevezh, who learned by Reb Chaim Volozhener as a young person.  This is from his Sefer מנוחה וקדושה, which has contemporary haskamos from the Netziv, the Pischei Teshuva, and Reb Betzalel HaKohen. It also has a modern haskama from Rav Shmuel Auerbach. So it's kosher.

This is from the end of the sefer. In the 1964 print, it got left out of the end and was printed on the second page and is titled

השמטות מחלק שני השייכים לסוף הספר

 כא כספנו במשקלו (שם מ"ג כ"א) בימים ההם עדיין לא היו בעולם מטבעות. וכל מסחרם היה או בנסכא של כסף או בכלי כסף.  ומזה ב' ראיות שזהו כספם. (א' כספנו) פי' אנו מכירים אותו בטביעות עין. ב' (במשקלו) שמשקלו שוה עם הכסף והאיש אשר על בית יוסף השיב להם. הכסף אשר הורדנו להם  אני קבצתי התבואה מהרבה בע"ב ולאחד היה הכסף טמון בתבואתו וכבר נתיאשו הבעלים.  ומזליכם גרם שבא המטמון הלז באמתחותיכם וזכיתם מן ^ ההפקר. מה תאמרו. אין השכל מסכים ששלש אלה יזדמנו יחד תמונה שוה, משקל  שוה,  עוד שלישיה שלא ירגישו בו המודדים,  הלא ע"כ צריך לתלות בנס, כי אני יודע בודאי ובברור (כספכס בא אלי) והנחתים באוצרותי.  בכן אין לתמוה אף שהנס למעלה מהשכל כי (אלהיכם ואלהי אביכם) הוא כל יכול לעשות בזכותכם וזכות אביכם (נתן לכם מטמון) השוה לכספכם והיה טמון באותה התבואה שנים הרבה  ואח״ז  בא (באמחחותיכם) ולא הרגישו המודדים. 

 I don't know how he deals with the evidence in Chazal to the contrary.

I had hana'ah from Reb Micha Berger's comment:

Or maybe coinage was invented in parashas Sheqalim, which is why HQBH needed to show Moshe what He meant visually.(Sheqalim 1:6, vilna 6a)
The mitzvah is simpler if Moshe could count half-coins, and not weigh random pieces of silver. But that doesn't mean that HQBH's revelation of the idea became commonplace for money.
Perhaps it wasn't until the idea of coinage or even of medallions kindled a lamp over some Lydian's head that the coin became a commonplace way of standardizing money.

He is suggesting that this is why Moshe Rabbeinu had to be shown the "matbei'a shel eish." Until that point, the concept of a uniform currency simply did not exist, and Hashem showed Moshe Rabbeinu that currency means that you take a certain weight of metal and you shape it and stamp it with an image that is unusual but reproducible, such that seeing the coin ensures that it is official, meaning that it reliably contains a specific weight of a particular metal.

So it could very well be that davka then was the first time mankind was introduced to the concept of a  minted, standardized, currency. 

There are still statements in Chazal about earlier coinage, such as in BK 97b, 

ואיזהו מטבע של אברהם אבינו, זקן וזקינה מצד אחד ובחור ובתולה מצד אחר

But it's possible that this was a medallion, not currency. After all, it was not produced by a government.

Reb Avraham Wagner points out the Gemara in Psachim 54b that implies that currency is ancient and fundamental to human civilization.

תנו רבנן שלשה דברים עלו במחשבה ליבראות ואם לא עלו דין הוא שיעלו על המת שיסריח ועל המת שישתכח מן הלב ועל התבואה שתרקב ויש אומרים על המטבע שיצא:

Rashi

עלו במחשבה - ונתקיימו:

UPDATE 1/8/23

I just came across the following. 

https://www.i24news.tv/en/news/israel/archeology/1673198534-study-reveals-silver-coins-were-used-as-currency-in-israel-3-600-years-ago

which reports new evidence that coinage was a means of commerce in the middle east  BEFORE AVROHOM AVINU WAS BORN, to say nothing of Mattan Torah. Shame on me for being impressed with what the archaeological community asserts to be clearly proven.

Relevant passage:

Silver coins made during the Late Bronze Age and used for payment were discovered at Tel Shiloh, north of Jerusalem, and at Tel Gezer, on the western slope of the Judean Hills, a new study revealed on Sunday. 

The coins were made in Anatolia, which today constitutes part of Turkey, and were apparently used as early as 17 century BCE. Another batch coins came from Tell el-Ajjul, presently located in the Gaza Strip; these were produced a century later, during the early Late Bronze Age, according to the new study conducted by the University of Haifa and the Hebrew University of Jerusalem.

"The transition to an economical method based on silver coins, which do not deteriorate and have a reduced volume and weight, presents many advantages and new possibilities which will certainly contribute to the urban and economic development of the entire region," said Dr. Tzilla Eshel, of the University of Haifa, who led the study.

The study also showed that silver coins continued to be used frequently, evidence of long and stable trade relations in Anatolia, something researchers were unaware of until now.

See also

https://nws.report/education/65292/ 

UPDATE JUNE 2023

My cousins from Israel visited us today. One of my cousins is David Gellman, an archeologist who  until recently worked for the רשות העתיקות, currently leading the excavations at the Givati lot. under the auspices of the Ir David foundation.

https://en.wikipedia.org/wiki/Givati_Parking_Lot_dig

I mentioned this issue to him, and he concurred that coinage was not known in Eretz Yisrael until toward the beginning of the Bayis Sheini. He said that the articles I cited above are not talking about minted coins, they were pieces of plain silver that were used by weight, not minted with any image. So the question remains unanwered.