If I wait on hiring my first specialist because I don't have any useful initial options, and I have a Foreman on my second roster of choices: can I hire that Foreman, then immediately promote them to an Engineer?
I ask because I trying to queue these orders for my queen, but it only gives me the choice to hire one of the first specialists. The second ones have no hire button to select at all.

Yep you can't do that. you have to hire one of the first three specs .