You could setup a custom rewrite rule using add_rewrite_rule and send these requests to a custom page.
Your URL structure could be /index-page/single-event-slug The rule would point all of the single events to a separate page where you can then set your template events-single.php.
Another option is to pass the events in as a query /index-page?event=single-event-slug or /index-page?event=123. You’d need to register this parameter with add_query_arg and then change your index template to use the event template via the template_include hook.