I take it this is the Pro version of Elementor that contains the Theme Builder and that allows you to read out custom fields from a custom post type?
Starting with version 0.8.0, if I remember correctly, the Event List plugin transitioned to using custom post types instead of using its own database tables. The following metadata (custom fields) can be stored with an event: ‘startdate’, ‘enddate’, ‘starttime’, ‘location’. These are the machine names, in the event editor they are labelled as “Date (required)” (one or two date fields depending on whether or not you checked “Multi-Day Event”), “Time” and “Location”.
I imagine that if you have access to Time and Location, you should also have access to the date(s). If you don’t, the reason may be that there is no one-on-one relation between the Date field in the event editor and a custom field in the back-end.
Do you perhaps see fields called ‘startdate’ and ‘enddate’? I don’t own Elementor Pro, so this is not something I could look up.