Creating custom taxonomy archive page

I have a custom post type of ‘Product’ and a custom taxonomy of ‘Product Category’. Some of the product categories have children and some have both children and grandchildren. Each archive page should have the children and grandchildren of the current category, as well as a list of products for each category.

I am having issues with this as most of the solutions I’ve found list just the children categories and not the posts or only go to the children categories, not the grandchildren. How would I write the query to achieve this functionality?