Jumping from X to Z do not show the progress and might be perceived as exaggeration. Received successive promotions from... or else is there any other structure can be used here.
You're likely to hear a native speaker use "through the ranks" here (from Oxford Dictionaries):
1 (of a privateor non-commissioned officer) receive a commission.
1.1 Advance in an organisation by one's own efforts.
"he rose through the ranks to become a managing director"
While the dictionary definition includes "to rise," it wouldn't sound unusual to me to hear "through the ranks" used without "to rise," for example:
He was promoted through the ranks [from clerk] to managing director.
Equally, you could use just "through":
PREPOSITION & ADVERB
4 North American [preposition] Up to and including (a particular point in an ordered sequence)
"they will be in London from March 24 through May 7"
The definition says "North American," but as a British English speaker it wouldn't sound out of place to me. For example:
He was promoted from clerk through to managing director.
It's also possible to use a phrase of "to work" if you wanted to add some emphasis to the person having been promoted through (hard) work:
Progress towards something better or ascend of series of ranks through hard work.
"she worked her way up to become a vice president"