Query Event Espresso events and order by start date time. You can use this in a custom template for displaying a list of Event Espresso events.

event_list_query_template_functions.php

<?php
function my_event_list_query_template_function( $query ) {
    if ( ( $query->is_main_query() ) && ( 'espresso_events' == get_post_type() ) ){
        $query->set( 'posts_per_page', 10 ); // or other value
        add_filter( 'posts_fields', 'my_posts_fields' );
        add_filter( 'posts_join', 'my_posts_join' );
        add_filter( 'posts_where', 'my_posts_where' );
        add_filter( 'posts_orderby', 'my_posts_orderby' );
    }
}
function my_posts_fields( $sql ) {
    $sql .= ', ' . EEM_Datetime::instance()->table() . '.* ' ;
    $sql .= ', MIN( ' . EEM_Datetime::instance()->table() . '.DTT_EVT_start ) as event_start_date ' ;
    return $sql;
}
function my_posts_join( $sql ) {
    $sql .= ' INNER JOIN ' . EEM_Datetime::instance()->table() . ' ON ( ' . EEM_Event::instance()->table() . '.ID = ' . EEM_Datetime::instance()->table() . '.' . EEM_Event::instance()->primary_key_name() . ' ) ';
    return $sql;
}
function my_posts_where( $sql ) {
    $sql .= ' AND ' . EEM_Datetime::instance()->table() . '.DTT_EVT_end > "' . current_time( 'mysql', true ) . '" ';
    return $sql;
}
function my_posts_orderby( $sql ) {
    $sql = ' event_start_date ASC ';
    return $sql;
}