The treaty required a council which was not NATO, it was the North Atlantic Council , the council underwent changes in 1950 and 1951 to split off the the organisation to become known as NATO. Most history books repeatedly use the term NATO members when they mean NAT members or NAC members.
The treaty makes no reference to any separate organisation, it is for different nations to co-operate together via the Council.
The first chairman of the North Atlantic Council was Dean Acheson from 1949 to 1950, he was Secretary of State for the USA, he was never employed by NATO nor had a NATO title.
The first NATO secretary was Baron Hastings Ismay in
1952 - who also uses the term NATO loosely in his 1954 book, the book indicates that the integrated organisation (ie NATO) came about in early 1951 after the 6th meeting of the Council.
The North Atlantic Military Committee were partly responsible for setting up aspects of NATO and had discussed it from late 1949 (as a minute title, not an entity) but I can find no evidence that there were personnel assigned to NATO or employed by NATO until later.
The North Atlantic Military Committee later became the NATO Military Committee, I thought this happened in 1955 but it appears to be much later(?). however again, many books etc use the term NATO Military Committee all the way back to 1949 - the simple proof against this is the minutes of their meetings until at least 1969 were titled "North Atlantic Military Committee".
The first Chairman of the North Atlantic Militarily Committee was Omar Bradley in 1949, his title at the time was
not "NATO Military Committee in Chiefs-of-Staff Session" as claimed retrospectively, he never had NATO title.
After a lot of searching I found the document detailing the setting up a joint budget for the creation of NATO dated July
1951 https://archives.nato.int/uploads/r/null/3/1/31702/D-D_51_177_ENG.pdfIf you can find any documents that were contemporary at the time that say otherwise I would be more than interested to see them, the NATO archive is full of stuff but difficult to plough through.