Hello, thank you for reaching out to Microsoft Q&A.
As you are seeing the message "This account does not exist" when trying to sign in, it is likely that the hacker removed your email address (alias) from the original Microsoft account, added it to their own account, and set it as the primary alias.
Since this is a @gmail.com address, you can add this same email as an alias to a new or different Microsoft account. However, the original Microsoft account appears to have been fully taken over by the hacker and most likely cannot be recovered, as they may have changed all the security information. This makes successful account recovery extremely difficult in this situation.
To add your @gmail.com address as an alias, sign in with your Microsoft account here (not the hacked one):
https://go.microsoft.com/fwlink/p/?linkid=864833
Select “Add an existing email address as a Microsoft account username”, then enter your @gmail.com address and check whether you can successfully add it.
You may reuse that email address (Alias) with a different Microsoft account. However, recovering the original or compromised account is no longer possible.
Meanwhile, see -
How to recover a hacked or compromised Microsoft account
My username and password have stopped working