@NazrinMaus
Stuff like grabbing a bow the first time and nailing several bulls-eyes in a row is just too much, at that point you'd think it would be standard for all recruits to try out each weapon type first to see if they have any talent.
Although it might be. Spearboy explicitly didn't want to use a bow because he felt it was a cowards weapon, so maybe he just said "I'm best at spears" and that was enough. (Especially since they probably were hiring spearcarriers at the time. During peacetime you just need people who can stand around and look cool and or/scary.)
If it hadn't been for the lords son asking (and the common knowledge that war is coming, and they need people who can kill well) they'd probably not have tested him.
I do agree that several noobie bulls-eyes are straining credulity, but it was still a pretty close range, so all he needs is a lucky first shot and then an ability to repeat the same motions and aim..