score:6
Having done a bit more research I have found this page concerning Awards and Promotions on a website regarding Werner Voss.
The website states that, as would be standard, all soldiers started of with the rank of "Soldat" or a unit based equivalent.
It also states:
Furthermore German Soldiers progressed through the ranks at a very slow pace. Typically a Soldat would not be eligible for promotion to Obergefreiter until he had been in the Army for six years.
Given that wiki page you quoted mentions that the standard conscription period was 2-3 years it would appear that NCO's of a rank exceeding Gefreiter (Obergefreiter and above) would be drawn from the pool on Long-Term Volunteer Enlistee's, as I mentioned in my comment.
EDIT I have found the following quote on greatwar.com, which also states that only career soldiers could be promoted.
A private in the German Army made about $5.10 US per month(30- day month), whereas a US soldier made 30.00/month w/an extra $6.00 if on "foreign" service. This was comparable to other European Army pay, and it taught the soldier to spend his money on necessities and hardened them for tough times in the field. Promotions were reserved for the career soldiers. Seldom did a two year recruit receive any rank. The unit commander made all recommendations for promotions when a vacancy appeared, which was then approved by the regimental commanders. One year volunteers with excellent records and at least 9 months service could be promoted.
Elsewhere in the article it states that on the outbreak of war all conscripts were obliged to serve until their 45th birthday (A reasonably standard measure, the same happened elsewhere). This change effectively put them on a par with the long term volunteers, as far as term of service is concerned.
Upvote:2
...Gefreiter was the only rank to which an enlisted soldier could be promoted.
The term "enlisted" is somewhat confusing here, as it translates poorly to the system of the German army.
In the Anglo-American system, you have two "classes": enlisted, and commissioned officers.
In the German system, you get three "classes": Privates, NCO's ("Unteroffiziere"), and officers.
If all you do is serving your conscription term (as the German army was a conscript army), you'll receive your basic training, then serve as a Private (Soldat / Gefreiter), and that's it. Insofar the Wiki page is correct -- you don't get promoted from Gefreiter to Unteroffizier.
So where do the NCO's come from? Easy: If you voluntarily extend your term, you'll receive your basic training, then receive NCO training, and rise to NCO rank (with accordingly better pay).
(This is, by the way, still the case in the German army today, even as conscription is suspended at this time. If you want to become Unteroffizier or higher in rank, you have to volunteer for a longer time of service and go through more extensive training.)
Of course, while the above was "the rule", there were always exceptions. A promising Private could be asked to attend NCO or even officer's training. Privates that had proven themselves in action could receive a battlefield promotion, although I would expect them to be sent back to receive the appropriate training at the next opportunity.
I was unable to come up with statistics on how often these things happened.
The best I could come up with during an ad-hoc web research was this paper (on page 21 ff.) talking about how, after WWI, the number of volunteers for officer's training did not meet the requirements. (The prestige of being a military officer had suffered badly, and a future in the shrinking military was an uncertain prospect in the early Weimar Republic.) So they filled vacancies in officer's training with promising NCO's and Privates, to the point where, in 1928, 3.5% of the officers corps (117 individuals) were former NCO's.
This is about NCO's reallocated to officer's training, not about Privates / Gefreite getting battlefield promotions to NCO rank. But I think it gives a general hallmark on both the existence and relative rarity of cross-career "jumping".