We do not generally recommend "search on x characters" as it may lead to a confusing UX. We would recommend trying to debounce sources as an alternative solution.
For Algolia extension version 3.11 and upward:
You can control the debounce request time and query length via the Autocomplete Settings in the Magento Admin -- Stores > Configuration > Algolia Search > Autocomplete.
You can find more information on these two settings here.
For Algolia extension versions 3.8 - 3.10.6:
You will need to override the functionality in view/frontend/web/autocomplete.js. Please note that you must override the functionality using Magento best practices. When getItems takes the query, you can check the query length and return an empty array or return the sources as needed.