So, the Search&Autocorrect plugin won’t work for this. It requires you to load all of the data you want to search through to the page to be able to search it. So, it’s great (both easy to implement and effective) for small lists (up to maybe as much as 100 things) but not at all viable for something this large.
The easiest option to implement that is somewhat workable is to use a RG to display the results of a search. Then, you have to “Do a Search for” (and perhaps different conditions that change the search) to lookup values in the database whose, say, title includes the search-input-field’s value. As such, when people type in letters, it’ll update the “Do a search for” and show a different set of results. This works well in that you have complete control over the UI and it’s fairly simple to implement. The problem is that the search doesn’t include advanced search options and it’s also noticeably slow - and sometimes frustratingly slow. I should also point out, somewhere in the forum someone (I belive @NigelG) explains how to implement this in a way that’s case insensitive (which is essential for usability in my experience).
The harder to implement option is to use something like Algolia. We custom built a version and got it working (so time consuming to implement) but it’s everything we could want in a search tool - super fast, advanced search (e.g., case insensitive, search within words, and lots more). Additionally, @levon recently released a plugin for Algolia search so I suspect that makes it much easier to implement.
If search is a key capability for your site (and it sounds like it is from what I recall reading from you in previous forum posts), then I’d strongly encourage you to look into Algolia.