special relativity - Postulate implies existence Lorentz transformation?

My textbook about Special Relativity says that the existence of Lorentz Transformation is guaranteed by the postulates of Special Relativity.

So, I'm assuming it's the first postulate we're talking about; laws of physics remain unchanged in different inertial frames.

However, how does this guarantee we can find the Lorentz Transformation between two inertial frames?

I've never doubted their existence, but I never thought of it as an implication of the first postulate.