A user calls you and tells you that a website you run is slow. What do you do?

Since you already said when you check the site yourself the speed is fine, this means that (at least for the pages you checked) there is nothing wrong with the server and it can serve those pages at a good speed. What you should be figuring out at this point is what the difference is between you and the user that reports your site is slow. It might be a lot of different things:

Is the user using a slow network connection (mobile for example)?
Does the user experience the same problems with other websites hosted at the same webhoster? If so, this could indicate a network problem. Normally this could also indicate a resource problem at the webserver, but in that case the site would also be slow for you.
If neither of the above leads to an answer, you could assume that the connection to the server and the server itself are fine. This means the problem must be in the users device. Find out which browser/OS he uses and try to replicate the problem. If that fails find out if he uses any antivirus or similar software that might cause problems

Check the server logs to analyse incoming traffic. Maybe a DoS attack or exceptionally high traffic. Interviewer told me to assume the server has normal traffic and no DoS.

If you have access to server logs you can analyze that, if not, then it is not your problem

But an assumption was that the CPU from which I tested my site loaded the site just fine