Let machine access my server after loosing machines public ssh key

I have currently lost my servers data and needed to restore the server from the backup. But the backup is too old for the server to know the machines ssh key.

                Server ----------------------------------- Machine 

(doesn't know public key of machine) --------------------- (has private and public key)

Machine tries to connect to the server, every 10 seconds. I can see the attempts in the log.

How can I give the machine (at least temporarily) access to the server? Disabling authentication doesn't seem to be possible with ssh?

The machine is too far away, so that i can't go there and get the public key again and can't give it a new key.

So is there any chance to let the machine connect to my server?

Note that the machine is out in the wilderness, so no human can easily access it.

No, loss of ssh keys means a user cannot log in.

If the private key is known, derive the public key from private. However, this doesn't help if the server doesn't have the public key, leaving the client still with no way to log in.

If a user who can become root can log in, use the privilaged account to install a new public key provided by the user.

If no one at all can log in remotely, use out of band management access to get a shell. Serial consoles, IPMI, a tech physically there to provide remote hands, however you need to get in.

And fix backups to cover the required recovery objective. Actually do restore tests.

Your only option is get a KVMoIP or similar device. If your colocating this thing a NoC tech can normally do this for you on "first come, first served" basis, at a fee or at remote hand rates.