Change Wordpress Instant Search page URL

How can I have the instant search field, results, and filters on a specific page template/URL?
I created a basic search page at /search following WP standards. After installing and getting everything set up with Algolia, it was my assumption that the search form on this page would be replaced with the instantsearch form and results.
However it does not. I am only able to get to the instantsearch page via /?s=foo.
My question is how can I make the instant search on /?s=foo work at /search/?s=foo?
Not sure if it is important but I have autocomplete working on a different page.

@natekrempel thanks for your question,

So my understanding is that you want to do a custom instantsearch.js implementation on a custom page.

This is currently not something the plugin can do out of the box.

However by inspiring from the existing instantsearch implementation, you could re-use existing Algolia indices.

Here is what you need to do:

Let me know if at some point you struggle, I’d gladly see what we can do to help.
Any live implementation during development would help us.