Yes, you can cancel your home or auto policy at any point.
All you need to do is email, call or text your agent and ask for that cancellation. If you want the cancellation back-dated, you will need to provide coverage documents from your new carrier. This is needed to cover the insurance company’s butt who you are canceling.
To further explain, when you cancel a policy the insurance company is no longer liable to pay your loss if you should have one. When you backdate a policy to be canceled, the proof of other coverage is needed as a way to show legal that we know you are covered and you are in good hands.