The initial state needs one-sided Laplace transform and several terms. A multi-order system needs several initial values. The response with initial state is zero input response+zero state response. The transfer function is only determined by the zero-state response, so the initial condition is 0. Of course, you don't have to set 0, just because the initial condition is generally 0. Looking at the differential derivative of Laplace transform, we know that setting 0 is a simple and idealized assumption.