At least Sergeant.
That's the minimal rank soldiers have in the special forces.
According to John Rambo's Dossier in the Ultimate Edition of the Rambo Movies it states that he was promoted in the field to a Sergeant during the Vietnam War
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A handwritten signature normally contains only first initials or forename, and surname. A printed signature or signature block may read, "J. Smith, Major, retired", "J. Smith, Major, retd", or "J. Smith, Major (retd)". The rank may also be abbreviated; e.g., Capt, Maj, Col, BGen, etc., depending on the degree of formality desired. Except in cases where the writer wishes to establish his/her qualification (e.g., a letter to the editor on a military matter), Captain is normally the least rank to appear as a postnominal honorific.
It is one rank below 2nd Lt. Here is a typical officer staff from archival records of 30th Mississippi Regiment, listed from company commander down to lowest officer rank. Company A, Neill Guards, of Carroll County,Captain - J. M. JohnsonFirst Lieutenant- J. W. S. MerrillSecond Lieutenant- J. T. StreaterThird Lieutenants- W. W. Conger, J. C. McMath.
Blackjack.
John "black-jack" Pershing
That was General John J. Pershing.