I wish I could give you a concrete answer, but it can vary depending on the article and the publication. Usually, if you submit it to a big enough publication, curation can happen within 24 hours. If you submit to Medium partner publications (Forge, Zora, Momentum, etc.), your story will be curated immediately after it is published.

Otherwise, if you self-publish, it can get delayed for over a month. Some of my stories have been curated (and some rejected) 50+ days after publication.