Bike to live,
Do you speak (or plant to learn) a high-demand foreign language other than French? Such as Arabic or Mandarin? Or are you planning on going into the medical field? If you do, there's another exception for you to consider:
The MAVNI program, which accepts non-immigrant/non-greencard foreign citizens into the US military:
link 1
The MAVNI (Military Accessions Vital to the National Interest) pilot program, authorized by the Defense Department, gives legal aliens with skills considered to be vital to national interest--doctors, nurses, and certain language experts--the opportunity to expedite the naturalization process by serving in the U.S. military.
Official US Army link
The program has been temporarily halted for now, though it will
reportedly resume this year after a new screening process is implemented.
While this program is for non-greencard holders, potential candidates for this program had to have been in the US for at least two years on another visa category such as a student visa or a tourist visa or a work permit.
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Still, have you ever thought about another alternative to the US Navy or the CF? How about the British Royal Navy? Canada is a member of the UK
Commonwealth of Nations, which means that we as Canadians can join the RN or other parts of the British military.
Direct quote from the
RN website:
British, Irish and Commonwealth citizens may join the Royal Navy or Royal Marines. However, certain career paths are only available to British citizens. See the link below for details.
However, the number of trades in the RN open to Commonwealth citizens such as Canadians, Aussies or Kiwis is limited and here is one example below:
RN aircraft handler rating
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Good luck in whatever path you decide to take.