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Almost immediately. Sometimes it helps to wait about a month so your new finance company can get the car title from the first finance company. It may take the state that long to process the title and get it to the initial finance company.
If you belong to AAA check with them about re-financing your new car. You may get a very competitive rate quoted. I did.
You can refinance as soon as you find a bank that is willing to finance you at a lower rate.
You can refinance as soon as you find an alternative finance source that will approve the loan. In the case of a new vehicle, do it as quickly as you can, so that you still qualify for a new car rate.