Looking to create a service account with access to a only a single Sharepoint site

Hi everyone,

I am looking to create a service account user that has access to a specified sharepoint site, but explicitly does not have permission to any sharepoint sites that are public to my domain. By this I mean any of the public teams and communication sites with "Everyone except external users" included in the membership list.

Is there any way to set up this service account that does not require restricting the domain-wide access to the existing Sharepoint sites in some way? Apologies if this is an already answered or strange question, I am admittedly somewhat new to all of this.