I confirm you need to have the meeple available.
For reference, rulebook page 11:
Promoting a Worker means to move it from your supply or your Player Board and place it on one of your company Milestones.
The only way to turn a meeple into another color is with the "Exchange a worker" bonus (the one with 2 workers and an arrow). For example, using the Purple special action when building a telegraph office.
Hope this helps,