

“of the sudden” (1570) actually predates “of a sudden” (Shakespeare) according to my OED as squinted at through the nifty magnifying glass. But it’s been considered obsolete for a long time despite having all of a sudden experienced a resurgence.
(Note, I modernized the spellings of “sudden” rather than try to switch focus back and forth)
Nothing wrong with “suddenly.” I probably should have used it in my previous comment. It’s just that sometimes you want to say “all of a sudden.” Especially at storytime. The extra time helps build the suspense. “Suddenly” is more sudden in that it just jumps in there. With “all of a sudden,” the subject isn’t ready but the listeners are.