How to get the inertia at the begining when using sklearn.cluster.KMeans and MiniBatchKMeans
It sounds like you are grappling with large data set sizes, for which I first suggest switching to mini-batch k-means. Mini-batch scales better so will be less frustrating.

Regarding apriori estimates of the inertia_, I suggest using a sample data set to approximate the inertia_ with appropriate margins of error. But, mini-batch may just preclude your need for apriori inertia_.

Hope this helps!