A static website with a dynamic search function? Yes. As alternatives to embeddable scripts from Google or other search engines, you can provide your visitors a custom search by indexing your content files directly.
Hugoidx is an experimental application to create a search index. It’s built on top of Bleve.
GitHub Gist for Hugo Workflow. This gist contains a simple workflow to create a search index for your static website. It uses a simple Grunt script to index all your content files and lunr.js to serve the search results.
hugo-lunr. A simple way to add site search to your static Hugo site using lunr.js. Hugo-lunr will create an index file of any html and markdown documents in your Hugo project.
Commercial Search Services
Algolia’s Search API makes it easy to deliver a great search experience in your apps and websites. Algolia Search provides hosted full-text, numerical, faceted, and geolocalized search.