If there is an event callback / observable missing in the MeshButton3D, please create a playground with the expected behavior, and we will be happy to look into it.
I am not sure how this will help in this case. The observable will notify before you will be able to add an observer. I am not against an observable, but it is not the solution in this case.
There are a few solutions, some require changes to the framework itself. I think the simplest would be to use the scene’s onNewMeshAddedObservable. In it, check if the mesh is ready, and if it is not, add the onReady callback. This way you have a generic solution for all meshes.