Click on the search icon at the top, and check ‘Search this topic’. Enter @Username and after a pause of a second or two it will provide a dropdown list of their posts in the thread. You can click on one to jump there, and then go back to the search box and click on another.
Also, if you see someone’s avatar anywhere in the thread, you can click on it, then on the filter button (‘x posts in topic’). It will then show only that person’s posts in the thread, which can be very useful. But it won’t work if the user’s profile is hidden. Yes, I’m looking at you, Heffalump!
You can do this with the operator ‘in:first’ which shows the topics they’ve started.:
@Username in:first after:2003 before:2008
More generally:
@Username in:first after:yyyy-mm-dd before:yyyy-mm-dd
If you want both before and after dates, you have to type the dates in manually, because the boxes in the advanced search only allow you to do one or the other.