As an administrator, you can ensure users on your network have access to Gmail.
Give users access to Gmail
Make sure your firewall rules connect to the following supported hosts and ports. Otherwise, users might be blocked or denied access from Gmail features. The asterisk (*) is a wild card, representing any value except a period.
Keep in mind
Even if you don't see activity at the above addresses, there could be future activity. Also, the IP addresses that various domain names use don't necessarily fall within any given range.
Techniques that Gmail uses to connect to Google servers depend on a number of things, such as the browser, browser version, and networking conditions. If your organization deploys Gmail add-ons, those might require you to authorize additional hosts.
Finally, other Google services could also use the same IP addresses that Gmail uses.