How to add new post or product with custom field in frontend?

Create page template for html form (not contact form) based on your requirements. Then you can I insert post by wp_insert_post method. After that, you can update custom post by update_field() method. Demo Code:-

if($_POST['title']){
 $arr = $_POST['title'];
 $post_id = wp_insert_post($arr);
update_field('extra_data', $_POST['extra_data'], $post_id )
}

Custom field is based on acf plugin. You can retrieve custom field data by get_field method or get_post_meta method.