You question is all over the place, it's difficult to understand what you are asking.
Based on what you've stated in your question and in comments I am interpreting your question as being “when were the European equivalent of Arabic numbers used with a common era calendar system to write dates similar to how they are written now?”
At the same time you appear to be trying to authenticate a coil dated 1234 using Arabic numerals.
If you are trying to establish the authenticity of a coin, supposedly dated 1234, forget the Gregorian calendar. It was introduced in 1582 and it is a refinement of the Julian calendar.
The Julian calendar was introduced by Julius Caesar in 46 BC and took effect in 45 BC.
Dionysius Exiguus, a Scythian monk, also known as Dennis the Short, is credited as
the inventor of the Anno Domini era, which is used to number the years of both the Gregorian calendar and the Julian calendar. He used it to identify the several Easters in his Easter table, but did not use it to date any historical event. When he devised his table, Julian calendar years were identified by naming the consuls who held office that year – he himself stated that the "present year" was "the consulship of Probus Junior", which he also stated was 525 years "since the incarnation of our Lord Jesus Christ".
That statement was made in 525 AD, the number zero had at that stage not been devised; it was introduced in India around 600 AD. Latin was the language of officials in western Europe and Greek was the language of officials in eastern Europe under Byzantine influence. If the year 525 was not written out in words it would have been written in either Roman or Greek numerals (DXXV or Φκε respectively).
The first mention and representation of Hindu-Arabic numerals (from one to nine, without zero), in Europe, is in the Codex Vigilanus, written in 976 AD.
In 999 AD Pope Sylvester II introduced an abacus based on the Hindu-Arabic numbers one to nine.
In his 1202 AD book Liber Abaci,
Leonardo Fibonacci brought this system to Europe. His book Liber Abaci introduced Arabic numerals, the use of zero, and the decimal place system to the Latin world. The numeral system came to be called "Arabic" by the Europeans. It was used in European mathematics from the 12th century, and entered common use from the 15th century to replace Roman numerals.
The familiar shape of the Western Arabic glyphs as now used with the Latin alphabet (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) are the product of the late 15th to early 16th century, when they enter early typesetting.
Fibonacci's introduction of the system to Europe was restricted to learned circles. The credit for first establishing widespread understanding and usage of the decimal positional notation among the general population goes to Adam Ries, an author of the German Renaissance, whose 1522 Rechenung auff der linihen und federn was targeted at the apprentices of businessmen and craftsmen.
Not knowing anything more about the coin you are trying to date. If the coin is of European origin it seems unlikely the coin or the date are genuine given the history of Arabic numbers and their European equivalents.
If however, the coin is of middle eastern origin, it may well be genuine. The year 2015 AD, or CE as some people prefer, is the same as 1436 or 1437 in the Islamic calendar or 1393 or 1394 in the Iranian calendar.
Using the Islamic calendar, the year 1234 using Arabic numerals would be 1813 AD/CE (2015 - 1436 + 1234) and from the Iranian calendar the year would be 1856 AD/CE (2015 - 1393 + 1234).