Ive come across something similar but not with just a simple cube, guess it will depend on how fast your computer is. It seems the engines frustum culling that culls objects out of view will cause bge to not pre-load objects. so at first frame start up I got around this by disabling frustum culling and then on the next frame re-enabling frustum culling.
This then stopped the camera stuttering for me when first viewing a lot of objects. I guess other game engines pre-load objects around the player within a short area, but we don’t have any sort of function like that built in.
Only weird thing about your case is you said objects continue to cause stutter when they enter the camera view frustum again which is odd as this doesn’t happen for me.
also a heads up simple shadows cause stutter on first game load also at the moment, oddly enough variance shadows are fine though, trying to get round to reporting that to tracker. you can do the frustum trick with the code I posted below, see if it works for you. fyi you have to disable occlusion culling in the menu settings for the script to work as that use’s some other method for doing frustum culling I think.
from bge import logic
scene = logic.getCurrentScene()
camera = scene.objects['yourcameraname']
camera.frustum_culling = True
camera.frustum_culling = False