To write a test, you have to first decide what the method or function looks like that you're going to test. You have to know what parameters to pass to it and what you expect to get back. THAT is what comes first, NOT the test. Tests can NEVER come first. The thing that comes first is the design which specifies what classes and methods are going to exist.
Not quite right (not entirely wrong either - It's Complicated[tm])
If you look at the first example in Test Driven Development by Example, you'll see that Beck doesn't begin with classes and methods. He doesn't even begin with a test.
The very first thing that he creates is a "to-do" list, where each of the entries in the todo list is a representation of a behavior (my terminology, not his). So we see things like
$5 + 10 CHF = $10 if rate is 2:1
These days, you'd be more likely to see this idea expressed as Hoare triple (Given/When/Then, Arrange/Act/Assert, etc). But what we have here is a reminder to the programmer that we want an automated check that measures the result of adding two different currencies together, and confirms that the result matches some specification.
In his exercise, his to do list includes a "simpler" test, which is the one he attempts first
$5 * 2 = $10
That same todo list also includes some other concerns the has about the design, NOT expressed in test form. Also, the list grows as he works through the problem.
In this sense, the test absolutely comes first. We write the test in a language to be consumed by humans. Translating the test into a language understood by the machine comes later.
In the second step, where we describe the test to the machine, things get messier. It is absolutely the case that, as we are designing the test, we are also designing the communication protocol that allows the test to measure what the production code does. So there's a certain amount of communication design that is happening in parallel with the "test" design.
But even here, the test is not specifying all of the classes that are going to exist, it's only specifying what it needs to perform its measurement. We describe a facade, but we aren't specifying what lies beyond that facade.
It can happen, as we design more of the system, that the facade we specify is used only by tests, as a way of communicating with a different underlying design of production code.
(Note: I say classes here for consistency with the question and with early literature, taken primarily from examples in Smalltalk or Java. Feel free to substitute "functions" for "classes" if that makes you more comforatble.)
Now, the most common case is that the facade is the production code; we don't typically add elements to the design until we have a non-speculative motivation for them.
"Unit testing" puts some strain on these ideas - how can you possibly write a unit test without first designing your unit boundaries?
The real answer is an unfortunate one -- Kent Beck didn't write unit tests. He wrote "programmer tests" (a term that got retconned in later) and called them unit tests.
Using the testing language of the 1990s (which is when all this mess started), a more appropriate term is probably "composite tests".
You've also got "the London School", that was trying to figure out how to TDD a particular design style; writing a test for that style requires a more complicated testing facade "up front" (roles and interfaces and stable substitute implementations and so on).
It can also be worth keeping in mind the setting.
(Disclaimer: this isn't something I witnessed first hand - think "based on a true story" rather than "facts")
TDD (and its parent idea "test first" programming in XP) are pushing back against "up front design" of the sort where you decide what the class hierarchy and relationships should be, and document them, before you actually sit down to write the code.
The core argument being that the design process needs shorter feedback loops; that we don't get deeply committed to a particular design until we've acquired a lot of evidence that it is going to work out OK.
All that said, yes it is absolutely the case that TDD, as a technique, works so much better in the hands of someone who is already good at software design. See Michael Feathers on the Look, Ma, no hands! era.
There is no magic.