Holidays can certainly be invented where they did not exist before. Mothers Day, Kwanzaa, Festivus, etc. are all examples of holidays of greater or lesser recognition invented in the 20th century.
"In the old days, before Mothers' Day was invented, Mothering Sunday was a feast of the Church"
"Mothers day was invented as a day to celebrate being a mom,"
or more cynically
"As history is clear, Mothers Day was invented by the greeting card & gift industry."
However, that's not the most common usage for holidays that came about more organically from historical roots rather than being deliberately instituted from scratch.
More common usage might be something like
"Memorial Day began as a way to honor those who died in the Civil War and has become a day to honor all American veterans who gave their lives [...] "(archives.gov)
"The dead of winter, when the longest night of the year takes place, has traditionally been celebrated as a time of renewal and reverence." (pbs.org)
"Halloween evolved from the ancient Celtic holiday of Samhain." (history.com)
"Halloween originated with the ancient Celtic festival of Samhain and is now a worldwide event." (also history.com)
"While Halloween originated in Europe, the holiday became the celebration we recognize today when it was brought to America by the early settlers" (nypl.com)
To sum up, for most holidays I'd use "originated" or "started", or even "grew from", but "was invented" can be appropriate in some cases.