‘Actually sending from an address’ is a concept that doesn’t exist.
If you want, you can limit the hosts that are allowed to send mail coming from your domain using SPF. Google does not control your domain so they can’t force, forbid or give your the option to do anything, but they do have a supported way for you to add their servers to the list.
This is all legacy though, if you set up a new alternative address you have to allow Gmail to send the messages through your own SMTP server.
I was just paraphrasing the concept of authentication for email domains. That's what DMARC is doing and why I mentioned DKIM and SPF.
I was unaware gmail free has a supported way to add the correct SPF records. Though thinking about it, even unsupported might be as simple as regularly scraping them from gmail and hosting them on your domains DNS records.
But they probably don't support DKIM through that (now legacy?) hack, which granted, isn't that important if emails come from a gmail mail server.
If you want, you can limit the hosts that are allowed to send mail coming from your domain using SPF. Google does not control your domain so they can’t force, forbid or give your the option to do anything, but they do have a supported way for you to add their servers to the list.
This is all legacy though, if you set up a new alternative address you have to allow Gmail to send the messages through your own SMTP server.
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