Add post with approval by the admin

Set New User Default Role to Contributor. Change user role of existing users as well, if needed.

UPDATE

Add this to your functions.php file. It’ll allow your contributor and author users to add WooCommerce products.
And then set default user role to contributor as I suggested before.

function wpse_306836_wc_custom_permission( $args, $post_type ) {

   if ( 'product' === $post_type ) {
      $args['capability_type'] = 'post';
   }

   return $args;
}

add_filter( 'register_post_type_args', 'wpse_306836_wc_custom_permission', 10, 2 );

Please note, some features like creating taxonomies, assigning them, uploading media files etc won’t work. You need to change permission for these as well.