Hi there
A View with filters initially shows all results until you apply filters to narrow down the results.
If you are using a View to generate both a map with markers and a list of posts then in your loop section you must be outputting both the marker and the fields that will appear in the list.
So your challenge is when the page first loads to show the markers but not the list (even though the same posts are being iterated over in the loop), and then when a search is made to show both.
So you don't need to do anything with the markers.
You would need to conditionally show the posts only when a search has been made.
You'll need to use wpv-conditional shortcodes for that, see: https://toolset.com/documentation/user-guides/conditional-html-output-in-views/
But what should you test?
Well, when you apply filters with a View, assuming your settings (at Toolset > Settings > Front-end Content) are set to "Enable history management setttings for AJAX custom search", then the URL will change to include certain URL parameters.
Here, for example, is what happened to the URL when I applied a distance search on my local test site:
<em><u>hidden link</u></em>
You can get the value of a URL parameter with the wpv-search-term shortcode (https://toolset.com/documentation/user-guides/views-shortcodes/#wpv-search-term), specifying which parameter using the 'param' attribute.
I haven't tested whether you can use a not-equals test for when a param has some unknown value (e.g. toolset_maps_distance_radius), but if needs be you could probably test for whether toolset_maps_distance_unit=km or somesuch.
Only display the list of posts when that is true.
Are you able to try that?