Creating product display in drupal commerce


I need to make product catalogue, that could be managed by non-admin user groups. What I am struggling with is new content type for products so that a user could not only create a node for existing product, but create absolutely new product without going to Store/Products.

I would also like to configure the system so, that via Add content/Product a user could only create new product and if user wants to edit existing product, he/she would have to find it as a node.

Thanks in advance.

Drupal version: