Routing path with Entity Reference field
The problem here is that controllers are specifically intended to return a result based on a given path. The result you want isn't dependent on a path, but rather on an operation performed on an entity.

What you'll want to use instead is one of the entity API hooks, found here: Entity CRUD, editing and view hooks

To respond to your entity being created, I recommend using:
hook_ENTITY_TYPE_insert()

function my_module_node_insert($node) {
  // Get ids for all Paragraph references stored in your field.
  $paragraph_ids = $node-&gt;get('field_paragraph')-&gt;getValue();
  // Get Paragraph storage handler.
  $paragraph_storage = \Drupal::entityTypeManager()-&gt;getStorage('paragraph');
  // Load Paragraphs from their IDs.
  $paragraphs = $paragraph_storage-&gt;loadMultiple( array_column($paragraph_ids, 'target_id') );

  // Iterate through your loaded Paragraph instances...
  foreach($paragraphs as $paragraph) {
    // Do your stuff to the paragraph.
  }
}


Similarly, if you need to update field_paragraph when you update your node, implement hook_ENTITY_TYPE_update().