Here is something quite interesting. I first read about this quite some years ago but lately this area of historical research through numismatics is gaining more traction.
Numismatics is the study and collection of coins, tokens, and other coin-like objects that people used as currencies throughout history.
Here are images of some coins from early Islamic history (as early as the 7th century AD).
In these early Islamic coins (above and below) there are depictions of the caliph's head or of human figures. There are arabic inscriptions on the coins like the 'bismillah' and 'laa ilaaha illalah'. Later the caliph's head and human figures would disappear from Islamic coins.
Above : Arab-Sasanian-style Umayyad coin minted under Mu'awiya I rule in Basra in 675/76 in the name of the Umayyad governor Ubayd Allah ibn Ziyad. (The reverse of the coin (on the right) has Zoroastrian features, including the crescent and star).
Here is a coin from the Umayyad period : https://www.numisbids.com/n.php?p=lot&sid=4345&lot=1789
which has crosses on it.
ISLAMIC, Umayyad Caliphate. temp. Yazid I ibn Mu'awiya, AH 60-64 / AD 680-683. Fals (Bronze, 20 mm, 3.83 g, 6 h), Arab-Byzantine type, 'Pseudo-Damascus' mint. Two imperial figures seated on throne facing, both wearing crowns surmounted by a cross and holding a cruciform scepter cross in their right hands; the figure on the right is holding a globus cruciger in her left hand; above, cross.
You can Google why the cross appeared on the early Islamic coins. For example this article.
The crescent and star symbol has a long history.
The crescent and star had also been used by the Persians (Zoroastrians).
The Persian / Zoroastrian symbol could have even represented the simple oil lamp:
