Certainly cheaper than the oil well and refinery needed to drive an ICE for free! This means there's a guaranteed crossover point and the relevant variable becomes the lifecycle of the car. Will you drive an EV enough to make up for the infrastructure costs?
This is true of electrical infrastructure as well. Solar is unique in that it's cheap enough that a family can consider slapping one on their roof for true self sufficiency, but that doesn't preclude industrial scale infrastructure (like nuke plants) from contributing as well.
You paid for the house, the solar and the new all-electric car though. So it depends on how long your commute is if it ends up cheaper or not.