add_action( 'woocommerce_after_shop_loop_item_title', 'custom_field_display_below_title', 2 );
function custom_field_display_below_title(){
global $product;
// Get the custom field value
$custom_field = the_field( 'start_date' );
// Display
if( ! empty($custom_field) ){
echo '<p class="my-custom-field">'.$custom_field.'</p>';
}
}