Sounds like what you want is mesh streaming -check out this thread:
Alternatively, you can get someway to that result by removing textures from your model and loading them after the main file. I do that on discoverthreejs.com. It doesn’t remove the loading screen but it does reduce the time it displays for quite a bit.
Check out the Sketchfab chapter in WebGL Insights for a more advanced and generic version - they load placeholder 16x16 textures with the model and then replace them with the correct textures in an order that isn’t visually jarring, starting with the opacity map.
If your model is relatively simple but has big textures this method will probably be as effective as mesh streaming and it’s a lot simpler!