This page on the FAA website has details on getting your student pilot certificate.
• Resident and US citizen student pilots follow Student Pilot’s
• Foreign student pilots (non-resident) follow the Alien Flight Student Program
It appears from your question that you should follow the same procedure as US citizens.
Refer to AC 61-141. Everyone must get a TSA screening before being issued a Student Pilot Certificate.
6.3 The Flight Instructor Verifies the Applicant’s Government-Issued Photo ID.
The flight instructor verifies the applicant’s identity and
enters information from the applicant’s ID. If the applicant cannot
present acceptable ID, discontinue the application process. Verify
that the applicant has entered a correct date of birth. IACRA will not
process an application unless the applicant is within 90 calendar-days
of his or her 14th birthday or older. If the applicant is not of
sufficient age, discontinue the application.
7.8 TSA Security Vetting and Temporary Certificate Availability of the Paper Method.
Provided the applicant is not deemed a security
risk and is at least 14 years of age, the Airmen Certification Branch
issues a permanent Student Pilot Certificate and mails it to the
applicant. Applicants must also wait to receive a permanent plastic
certificate in the mail.