In coreFORCE, in Orders > Setup, there are fields which will be automatically populated with your domain name and will show you how to connect your product feed to Google.
This video from Google explains the process of adding a product feed to the Google Merchant center. For coreFORCE, you would select the Scheduled Fetch option instead of Google Sheets or Website Crawl, and enter the URL from the Setup page (https://<your domain name>/googleproductfeed.php).
Note that Google does not allow certain categories of products on their site, including firearms and ammunition. See the link below for details. The coreFORCE Google product feed will automatically exclude any products marked as firearms or ammunition and anything that must be shipped to a FFL dealer.
If there are additional products that you need to exclude from your Google product feed, you can do so by creating a category with the code EXCLUDE_GOOGLE and adding it to the products that you don't want to be shown on Google.
Google Shopping Ads Polices - Prohibited Content - Dangerous Products