functions.php

<?php

/**
 * Display Posts - List upcoming events from The Events Calendar
 * @see https://displayposts.com/2019/01/04/display-upcoming-events-from-the-events-calendar/
 */
function be_dps_future_events( $args, $atts ) {
  
  // Only run on event queries
  if( 'tribe_events' != $args['post_type'] )
    return $args;
    
   $args['order'] = 'ASC';
   $args['orderby'] = 'meta_value';
   $args['meta_key'] = '_EventStartDate';
   $args['meta_type'] = 'DATETIME';
   
   $args['meta_query'] = array(
      array(
        'key' => '_EventStartDate',
        'value' => date( 'Y-m-d H:i:s', current_time( 'timestamp' ) ),
        'compare' => '>'
    ) );
     
     return $args;
}
add_filter( 'display_posts_shortcode_args', 'be_dps_future_events', 10, 2 );

Is there a way to display the event start date?

There is an important typo in the snippet as of writing! Unless/until the item below is addressed, this snippet won't actually do anything.

if( 'tribe_events' != $args['post_type'] ) (at the start of the function) needs to be if( 'tribe_events' != $atts['post_type'] ) (effectively swap $args for $atts) since we're checking the shortcode attributes & not the query arguments for what post type has been specified (which it then proceeds to adjust the $args for the query accordingly if the post type specified via the shortcode's attributes is tribe_events.)

@carljbusch

Is there a way to display the event start date?

I know this is late, but this might still be helpful for others.

I use the following (or similar) for that sort of thing: https://gist.github.com/KZeni/1c9d2204f553457a8b034696d4e472ec