Progressive loading and mesh streaming is not currently a built-in feature, but it would be fantastic to have and is definitely achievable.
A method using POP buffers has been developed for WebGL without relying on three.js: & https://github.com/thibauts/pop-buffer
You can see one of the demos here:
Hopefully, in the future, we will also have a nice progressive loading system like POP buffer (or a similar alternative) for three.js - it's on my/our to-do/wishlist as well, but there are many tasks to tackle before that happens.. however, I wouldn't mind if someone beats us to it!
While Three does provide a basic LOD mechanism to assist with rendering load, it doesn't specifically address loading time: &
For a straightforward solution, you could create low and high versions of your models and implement custom loading logic to initially load the low version and display it, then gradually load the high version afterward.
We've employed this approach in a project before, and it worked smoothly as expected. The only downside we observed was an increase in total loading time for the high version. Nevertheless, since the low poly version can be very small (untextured with only vertex colors), it's manageable until the high-res version loads.