Sending big objects (especially multiple big objects at once) to the GPU will incur overhead. Sometimes that overhead is enough to drop frames.
The overhead comes from lots of places. Getting the data into the GPU, making the texture ready, (possibly) compiling the shader, etc…
How to fix it largely depends on what the actual cause is but step one is to reduce the size or the count of objects you add in one frame. You don’t say how big “big” is or whether it’s already only one at a time.
For Mythruna, I had to spend a lot of time tuning my “chunk” size to balance between generation time, culling efficiency, and frame drop. In the end, frame drop was most affected by how many chunks I added at once… so I only add one Spatial per frame.
Anyway, you can see all of this in action in the IsoSurfaceDemo which generates terrain on the fly and generally does it without frame drops. I even wrote a whole paging library to help others do similar.
Paging library it uses: