Can I get my student pilot certificate at the same time I take my initial flight physical?

No. Effective April 1, 2016, Aviation Medical Examiners (AMEs) are not authorized to issue combination Airman Medical and Student Pilot certificates to applicants. To obtain a student pilot certificate, you must complete an application through the Integrated Airman Certification and Rating Application (IACRA) or by paper using FAA form 8710-1 and submit it to a Flight Standards District Office (FSDO), an FAA-designated pilot examiner, an airman certification representative associated with a part 141 flight school, or a certificated flight instructor. The authorized individual will process your application and submit the required documents to the Airmen Certification Branch. Once reviewed by Airman Certification Branch, the student pilot certificate will be mailed to the address provided by you on the application.