WP Rocket has a feature to delay JavaScript execution:

Using this feature with Search & Filter can result in our search & filter fields not displaying at all.
To work around this, we can add some rules to exclude our JavaScript files and objects.
In the Excluded JavaScript Files section:

Add the following rules (copy & paste):
/wp-content/plugins/search-filter-pro/assets/js/frontend/frontend.js
/wp-content/plugins/search-filter/assets/js/frontend/frontend.js
/wp-content/plugins/search-filter-elementor/assets/v3/js/frontend.js
/wp-content/plugins/search-filter/assets/js/vendor/flatpickr.js
window.searchAndFilter
window.searchAndFilterData
window.searchAndFilterApiUrl
Once they’ve been added and saved, Search & Filter should work again as normal.