I've flown with the military for a long time and I've seen good FEs that didn't come from MX and bad ones that did. The AF doesn't allow first termers in the FE seat, they must crosstrain. I have seen guys move from LM to FE though, again some good, some not.
I think an aptitude test is used at some units, if not all, to determine if the guy has the math and mechanical skills to be an FE.
Good LMs can be first termers, but for the most part they have to want to be LMs. If you force a guy into it, he's not going to do it very well and there are some problems (like airsickness and no definite schedule) that make life a little difficult, especially if you don't want to fly.