Shopify provides a method to hide products in your store from Google and other search engines. It is documented here - https://help.shopify.com/en/api/guides/updating-seo-data#hide-a-resource-from-search-engines-and-sitemaps.
Using this method also hides the product from Shopify's site search.
It's pretty simple if you are comfortable with metafields. You need to set the seo.hidden metafield for the product to '1' (stored as an integer). This is easy to do if you are using the ShopifyFD Chrome plugin.
I also like to edit metafields is the bulk editor. If you do though, you'll need to specify the integer format of the metafield in the URL. Otherwise it will store it as text. And the value for the integer format is 'number', which is a slight inconsistency which can cause some confusion. So here's the URL to use:
https://yourstore.myshopify.com/admin/bulk?edit=metafields.seo.hidden:number&resource_name=Product
I hope that helps.