Indeed, there is a solution available by utilizing custom events triggered within the dataLayer.
If the particular div you are seeking to identify is present on DOM Ready and is labeled 'mydiv', then simply check for its existence and push an event to the dataLayer like so:
if(document.getElementById('mydiv')){
dataLayer.push({'event':'mydiv_exists'});
}
This code can be placed in various locations, but it may be most effective to incorporate it into GTM as a 'custom HTML' tag that triggers on all pages.
In addition, you can set up a trigger of the 'custom event' type to listen for the event named 'mydiv_exists', enabling further customization for tags to activate upon this trigger.
If necessary, you can also include other data into the dataLayer simultaneously with this event.