Is there a way to add an SSL certificate to a domain which we don't have control over?
If you do neither control the host in question nor the DNS zone the host's records are in, there's no way to accomplish what you are asking.
If you have control over DNS then you can set up your own reverse proxy (nginx, haproxy, AWS ALB etc.) and use it to terminate TLS/SSL and pass all the traffic to the existing backend. Alternatively, you can even set up a CDN (Cloudflare, AWS CloudFront etc.) and point it to the existing server.