New packages will be crawled within ten minutes.
Existing packages will be crawled every hour.
The search index is updated every five minutes. It will index (or reindex) any package that has been crawled since the last time the search indexer ran.
Yes, you can click the "Force update" button on your package page if you are logged in as a maintainer. The recommended way is to set up the GitHub hook, you can find the URL and instructions on your Packagist profile page.