We study a Coordinated clinic and surgery Appointment Scheduling (CAS) problem for in-advance scheduling of surgical patients. Our models seek to provide timely access to care by coordinating clinic and surgery appointments to ensure that patients can see a surgeon in the clinic and (if needed) schedule their surgery within a maximum wait time target based on patient classes. There are different types of uncertainty including the number of appointment requests, whether a patient requires surgery, and surgery durations. We develop an Integrated Multi-stage Stochastic and Distributionally Robust Optimization (IMSDRO) approach to determine the optimal clinic and surgery dates for patients such that the access target constraints are satisfied, and the clinical and surgical overtimes are minimized. The IMSDRO approach synergizes multi-stage stochastic optimization with distributionally robust optimization to simultaneously incorporate multiple types of uncertainties by including stochastic scenarios for appointment request arrivals and ambiguity sets for surgery durations. Several new transformations are introduced to turn the nonlinear model derived from the IMSDRO approach to a tractable one, and a constraint generation algorithm is developed to solve it efficiently. We propose a data-driven Rolling Horizon Procedure (RHP) to facilitate implementation. We use case data to assess the performance of our policies. The results suggest that our policy can significantly improve surgical access delay times compared to the current practice. Our methodology is not limited to a particular setting and can be applied to other service industries where access delay matters.