First the time frame for getting to actually drive is dictated by
a. the number of seniority employees ahead of him
b. the number of available slots in the center he is working.
The time frame before he gets an opportunity to qualify is also dictated by the size of the center. In one of our buildings, which is a smaller extended center, we have people who have been waiting 5-7 years for an opportunity. In our bigger hub we have people who have gotten the opportunity within 6 months to a year due to the fact we had a lot of feeder routes put in and in turn we had to promtoe a lot of package drivers to take their place.
Another thing to consider: under our agreement with the union in this area of the country a person goes through a one week training class. From there he is placed on a list as "ready to train". Once he meets this level he still may have to wait a while until the center says they are ready for a driver. Once the center says this, the person gets 30 days to qualify - learning the route, meeting performance measures, no accidents, etc. If he makes it through the 30 day period he is consider "full time" and starts on his 24 month pay progression period.
If he fails any part of the 30 day training, he is disqualified and can try again in a year, but he only gets two more opportunities to qualify.
If he doesn't pass in 3 total tries he is done for life and will never get an opportunity to drive. He would have to try to qualify for an article 22.3 full time job at that point.
You didn't say what part of the country you were in, but this how it works under the Southern Conference of the Teamsters contract.