Can I recover a lost domain if I can prove that I can send emails from email addresses in this domain?

Last year, I did not renew my domain by mistake. And he was taken by someone else.

The name servers were never changed, so I could use my GSuite registered with this domain for one year (for free).

Now the domain has expired and has entered the ClientHold status (even if the expiration date indicates an extra year), so it is no longer resolved, but I can still send emails from of it.

Is there anything I can do to get it back as soon as possible?
This does not seem to be used at all (as I said, the name servers have never changed in a year) and I would certainly use it.
Does it help if I can prove that I have outgoing emails? (I can send emails from all accounts in this domain)