I could be totally wrong, but I highly doubt you will find any setting that would sponsor a green card for a PT. You should be fine getting a work visa, but I'd be surprised if they'd sponsor a green card. If I'm wrong though, let me know!
It would not make sense for clinics to sponsor a DPT student . They would rather sponsor a PT from another country who is already able to work/take US board exam soon or have already taken the boards. You will not be able to work as a PT while you are a DPT student, so I do not know how clinics/hospitals would be interested in sponsoring your green card. You could work as a PT aide for a minimal wage, but clinics can find aides here without getting into all tedious work with greencard responsibilities and paperwork. It would probably make more sense to look for greencard sponsorship by the end of your DPT program.