I doubt it, since minors generally can't sign contacts.
Check to see if your state allows used car sales from parents to children without sales tax. If so, you could then have them reserve. If you can't get Tesla to agree to transfer the reservation (this is one case that might make sense), your parents could take delivery and sell it you.
You'd lose the income tax credit in a resale (cars purchased for resale can't get the tax credit), but at 19-20 years old, you probably wouldn't have enough income to claim much of a credit, anyway.