@Teepster87 @britzen may have slightly more info/guidance?????
The CDC epidemiology elective is by application only. The app opens in February for externships the next year (as in, I just applied in 2021, hoping for a spring 2022 externship). Here's the details:
Epidemiology Elective Program Homepage | CDC
Other people I know have done rotations with the CDC One Health office, but I don't know how they got them - I think they networked their way in. They took externs on short notice last summer.
The easiest way to get your foot in the door at USDA is to apply to do one of their summer internship programs. Other externships are case by case through the office that they are in I think (as in there is no central process - you make a connection and that office sets you up to work with them). Some places are more receptive to hosting interns than others.
You can reach out to USDA at any time really, but try to give yourself a decent amount of lead time (months) to deal with on-boarding paperwork if you are not already an intern for them. You will have to do a background check, fingerprints, etc. The process can take several months, and many offices aren't willing to do it anymore because the HR process has been made so difficult that it's not worth it for them to host externs. I know the office I intern for won't accept externs at all anymore because of how onerous the HR process has become, but another office I am doing a detail with for the Spring just hosted an extern for 3 weeks so clearly they were willing to make it happen.
@Teepster87 may have thoughts about what that looks like from the both sides.
State vets office, state wildlife vets, etc have been much faster and more flexible in my experience.
As you network in school, if you see something that you think may interest you, contact them and ask how far in advance you will need to contact them for possible externships. There are some that you need to plan a year or more in advance (CDC epi elective, Southeastern Cooperative Wildlife Study, a lot of zoos, etc). To do that you are going to need to design your clinical year schedule around those electives.
There are many others that you can schedule a few months out without too many issues as long as they have a spot, so you can wait until you have your clinical year schedule to contact them.
This was a very wandering answer to say - contact any placement you think you want to ask them! It varies a lot.