How to set a type depends on function arguments in typescript?

I think using a generic conditional type this way as a function return is perfectly fine. As you've noticed, the compiler is unfortunately unable to verify that a particular value inside the function implementation is assignable to such a conditional type dependent on an unspecified generic type parameter; this is the topic of microsoft/TypeScript#33912. Until and unless that issue is addressed, you will have to shift some of the burden of type safety from the compiler to you, such as with type assertions, or, as you've done, a single-call signature overload.

As for the implementation of getTestConfig(), you can't say that config is a TrueTypeConfig | FalseTypeConfig because it doesn't have enough properties to start with. At best you could say it's type Config and then later narrow it to one of the desired types.

Instead of initializing config in stages, which is hard for the compiler to verify, I would just use something like Object.assign() or object spread to initialize config all at once:

function getTestConfig<T extends boolean>(type: T, id: string, password: string): T extends true ? TrueTypeConfig : FalseTypeConfig;
function getTestConfig(type: boolean, id: string, password: string): TrueTypeConfig | FalseTypeConfig {
  return {
    id: getRandomData(id),
    password: getRandomData(password),
    ...(type ?
      {
        emailId: getRandomNumber(1, 100),
        paymentId: getRandomNumber(1, 100)
      } : {
        documentId: getRandomNumber(1, 100),
        buyerId: getRandomNumber(1, 100)
      }
    )
  };
}

That should compile cleanly.

The only other way I can imagine to do a return type that depends on input parameters more safely (which precludes overloads entirely) is to try to use a lookup type for the return. I tried this and it's really ugly/impenetrable and relies on coercing boolean values to their equivalent string via TS4.1's template literal types. I won't even include the code in the text here, since I don't recommend it. It's included in the Playground link below if you really care, and I'm happy to explain it if you want. But I'd say that a generic conditional type is probably the best solution for now.

Playground link to code