To answer your question, yes, I think it should be possible to enable the Elasticsearch connection without reinstalling the whole Magento project. Just make sure your Elasticsearch is installed properly, the version is compatible with your Magento install (according to https://devdocs.magento.com/guides/v2.4/install-gde/system-requirements.html, accepted Elasticsearch version should be 7.x).
Now, in order to connect Magento to the Elasticsearch service, run the following commands:
php bin/magento config:set catalog/search/engine elasticsearch7
php bin/magento config:set catalog/search/elasticsearch7_server_hostname <elasticsearch_hostname>
php bin/magento config:set catalog/search/elasticsearch7_server_port <elasticsearch_port>
Just make sure you replace the hostname and port placeholders with the actual Elasticsearch connection data. Flush caches and you should be good to go.