You can't access the files directly, it is not possible.
Elasicsearch is REST based, to see what you have stored without using a visualization tool like Kibana, or something like Grafana, you would need to make a request using the Search API and work with the result.
For example, if you have an index named nginx-logs and want to see what you have stored a simple GET request using curl would return you some data.
curl -X GET "localhost:9200/nginx-logs/_search?pretty"
You also can use the Query DSL to make more complex queries with filters and things like that.
It is also possible to write some tool or script using one of the clients to retrieve and parse the logs.