How to Set Up a Redirect with SSL for Internal Use?

I'm trying to figure out a way to use a service like ZeroSSL to create a valid SSL certificate for a domain that I don't have authority over. The goal is to have a local server (for example, Nginx) redirect traffic from "www.google.com" to our internal search engine via a 301 redirect. This is necessary for devices that frequently switch between internal and external networks, requiring a trusted SSL certificate for a smooth transition. While I could set up my own Certificate Authority (CA) to create self-signed certificates for a few hosts, that seems a bit excessive for just three domains. I'm hoping someone might have a more practical solution!