Based on the following statement published on the official WooCommerce website, you can’t override the archive.product.php file in Genesis :
If your theme has a woocommerce.php file, you will be unable to override the woocommerce/archive-product.php custom template in your theme, as woocommerce.php has priority over other template files. This is intended to prevent display issues.
If you want to customize the WooCommerce archive-product.php template, copy this file (keep same name) and place the copy in the child theme’s woocommerce folder, ie themes/my-child-theme/woocommerce (Your theme may not have a ‘woocommerce’ folder, in which case create one.) The version in the child theme’s woocommerce folder will override this template, and any future updates to this plugin won’t wipe out your customizations.
However, this method no longer works in Genesis child themes.
There’s at least 2 ways you could still use a custom woocommerce archive template in Genesis.