Should all assets be loaded immediately?

I am working on a project which will have a rather large world with many static objects, all of which generated when the game first starts. Should I add all objects immediately or only when the player is within a certain range of them?

Depends on how many objects there are really. Just note that loading the object from the assetmanager and actually uploading it to the GPU are two separate things. To make sure the objects are all in the GPU set the cull hint to never, attach them and let one frame pass.

Also depends on the game,

in a turn based strategy game, a slight delay upon chanign rounds is finer,
in a fps it would be way more annoying.