WooCommerce [products] shortcode order by product attribute

I’m using the default WooCommerce [products] shortcode as indicated in the example here https://docs.woocommerce.com/document/woocommerce-shortcodes/#section-7 and the default orderby values are only:

– date – The date the product was published.
– id – The post ID of the
product.
– menu_order – The Menu Order, if set (lower numbers display
first).
– popularity – The number of purchases.
– rand – Randomly order
the products on page load (may not work with sites that use caching,
as it could save a specific order).
– rating – The average product
rating.
– title – The product title. This is the default orderby mode.

But I need it to be ordered by a custom product attribute present on all of my products named custom_index. Is it possible to filter the [product] shortcode to achieve a custom orderby from a product attribute?

Already tried [products orderby="custom_index" order="ASC"] and hooking into woocommerce_product_query, but it seems none works.