The Good Morning/Good Day formula is pervasive in European languages, but is presumably not universal, and presumably it has not always been around. Do we have any evidence of when and where it first originated?
I don't have any information on Latin/Early Romance (which would be a prime vector for such an expression to have diffused through Europe). And I hope someone else can answer for Latin!
But I have stumbled across an early attestation of "Good day to you" in Greek—which seems to indicate that the expression was at the time regarded as novel.
The Life of St Auxentius (written in the early 6th century AD, in an episode preserved in two linguistically archaised versions from the 11th century) records the saint making fun of a villager for greeting him with "Good day to you": he retorts "and a Good [entire] season to you", and grumbles that the villager should have asked for a blessing instead. One of the two versions explicitly calls the expression "local", which implies "vernacular".
By the 10th century, the expression was commonplace in Greek: it is reported in court ceremonies in the De Cerimoniis.
I have found no earlier instance of a "Good Day" expression in Greek than the 6th century.