“add_post_type_support” with Custom Post Type & ACF

You need to use filters to hook into manage_posts_columns and manage_posts_custom_column which will let you add the table heading and dates. The filters are slightly special as you need to include the name of your custom post type

manage_{$post_type}_posts_columns
manage_{$post_type}_posts_custom_column

where {$post_type} in your case is conferences

// Add the table heading
function conf_columns_head($defaults) {
    $defaults['conference_date'] = 'Date';
    return $defaults;
}

// Add the conference date
function conf_columns_content($column_name, $post_ID) {
    if ($column_name == 'featured_image') {
        echo get_field('conference_date', $post_ID)
    }
}

add_filter('manage_conferences_posts_columns', 'conf_columns_head');
add_action('manage_conferences_posts_custom_column', 'conf_columns_content', 10, 2);

Untested code, but that should get you started.