You define an audience. You split it. You test and measure the result.
What component of that strategy doesn't work for new visitors? Many eyeball vendors (Google, Facebook, heck traditional TV and other media!) are set up precisely to allow for such cases.
One tool with FB lift tests is to make a lookalike audience. FB will then split that audience in two for you so you have a test and control group.
The original test required two ad accounts and keeping your overall advertising static (not changing anything) for the duration. Today it is much easier and has a lot more features.
Google does a search lift test with YouTube as well. You can run a large set of ads against an audience in YT and google will either suppress them for a subset. Then you can see your overall organic lift based on your video ads.
FB can track ads using clicks and view through. With a control group, you can only use view through. I am just skeptical of how it is a fair test especially when FB has an interest to prove that ads work.
YouTube brand lift is an indirect measure that is hard to translate to actual sales to see if the ads were cost effective.
The math is fuzzy when measuring marketing ads and it is real hard to be truly scientific.
The concept, principles, and methods, are taught in the context of marketing and advertising academic programmes.
See, e.g., ADVT5440 and ADVT5501 at Webster University, for example:
This course emphasizes the importance of critical thinking in the planning and development of message strategy for advertising and other marketing communications tools. Class discussions explore the decision making process and development of criteria for evaluation of alternative message strategies.
It is something that could work for retargeting existing users but doesn't work for acquiring new visitors.