Our scrum team of three developers has a dedicated tester. At the moment the tester is ostensibly waiting for something to test for most of the first week of our 2-week sprint. We typically do our first release of the sprint deliverable around the Thurs or Fri of sprint week 1. At this point our tester can "test" the embryonic software.
This begs the question in my mind - how much value is functional testing like this adding, so early in the development of the deliverable?
At this stage (end of sprint week 1) in development there are usually significant bugs / functional omissions which would be rectified if testing was postponed by only a couple of days (say to week 2 of the sprint).
What is best practice in this case?
While you mention Scrum, a good management practice, you don't describe which testing practice you're using.
If you're using best practices, you should be using Test-Driven Development.
Test-Driven Development means that the testing must be done from the very beginning. The programmers must write tests and fill in classes that pass those tests.
The tester should be writing functional tests on day 1 which the application absolutely fails to pass on day 1. Eventually the application starts to pass those tests and you can call your sprint done.
If you're not doing test-driven development, you should be, and your tester should be writing integration test cases.
If your tester can't code, teach them to code. You must have a tester who can code. And make them start coding functional tests on day 1.