You can try emailing field vets directly or emailing the field operations supervisor to ask. For USDA, the district supervisors are usually easy to find online, although there is a list out there somewhere that has an org chart with every field vet in APHIS.
They probably won't respond but someone I work with had mentioned having undergrads shadow before so it is possible.
You might have the best luck with FSIS honestly, since they have more trouble recruiting and retaining vets, they may be more open to it. (Although shadowing in a slaughterhouse may have the opposite effect on your motivation...)
If you are close enough to an HQ or hub office I'd also suggest asking to shadow in an office- they cycle through a lot more interns (volunteer and paid) so are more likely to have an HR person that would know what to do with you in terms of application / paperwork needed.
I'd also suggest contacting your state vet office- similar experience for your resume, but probably more likely to respond to your inquiry.
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