Traditionally, the concept of the cross being made of olive wood originated in the writings of early Christian writers, such as Cyril of Jerusalem in the 4th century. However, these references are based on pious legends rather than historical accounts.
The most common narrative is that the cross was made from the tree that grew on the site of the Garden of Eden, where the Tree of Knowledge and Tree of Life were believed to have been located. According to this tradition, the wood from the Tree of Knowledge was used to make the cross, symbolizing redemption and the triumph of good over evil.
However, it's important to note that these legends are not supported by any historical evidence or biblical passages. The specific wood used for the cross remains unknown and is a matter of religious belief and tradition.