Watkinstam --- do you still have the business card or contact information you received at the interview? You should reach out to the NUPOC office at Naval Recruiting command --- I don't have the data handy at the moment (away on travel for several weeks for work) but I'm certain that you've got at least a tentative date in place.
In general, we try to ensure that everyone gets at least a few weeks to get their affairs in order prior to going to ODS/OCS --- but it can be quite a bit longer depending on how the class dates line up.
If you graduate in May, I would expect you to go to ODS in June or July --- but again you should reach out and get the real answer. This is outside my swim lane, as I mostly deal with the pre-interview/accession side of the program.
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No data on the gap between ODS and NNPTC --- I would expect at least a couple of weeks. You could probably take a bit more, but you would be using leave (which you should have a boat-load of --- so not big deal there I suppose). That's also out of my swim-lane (it's deep and narrow, apparently!)
