What word means "an event that can occur without an appointment/schedule"?

To amplify an earlier comment:

impromptu = done or said without earlier planning or preparation

Cambridge dictionary

Made up adjectival examples:

"We are just heading for an impromptu meeting. Care to join us?"

"The meal was delicious even though it was impromptu."

The word may also be used as an adverb

without preparation or planning

"Roy came up and just started speaking impromptu"

Oxford learners

It comes from:

impromptu (adv.) 1660s, from French impromptu (1650s), from Latin in promptu "in readiness", from assimilated form of in- "into, in, on, upon" (from PIE root *en "in") + promptu, ablative of promptus "ready, prepared";

Etymonline

Because of its long usage and its foreign flavour, the word has the desired more formal feel than "drop-in".