Advertising third-party site listing on Google Ads

I have a client who would like to advertise their service on Google Ads, but they do not have a website. They are interested in getting more calls.

While I can offer to create a website for them, it would be a lot easier / cheaper for the client if we could create a listing on a third-party listing site and advertise that listing on Google ads instead.

Would that even work / be something that Ads can be set up to do ? If so, is the efficiency going tank a lot compared to a dedicated website ? Is there any other workaround this problem, different from the solution I am currently thinking about ?

Any help will be appreciated !