Is that to electrical code anywhere? To do that, you would have to convert the white neutral wire to a hot wire and use the unshielded ground wire as neutral. It would work electrically, but I wouldn’t confess to anyone that I did that.
I realize this has been covered above, and OP already has the wall connector installed, but I write the below for others that may come across this.
Tesla mobile connector or wall connector do not require neutral.
It is common for appliances that are strictly 240 volt, like the Tesla connectors, to use two conductor, with ground, cable.
Also, if you can it is a really good idea to repurpose a dedicated 120 volt garage outlet to a NEMA 6-15 (15 amp circuit with 14 AWG wire) or NEMA 6-20 (20 amp circuit with 12 AWG wire). Wish I had thought of that.
But be damned sure that 120 volt outlet in the garage is a dedicated outlet (no other outlets on the same circuit). And be sure to install a 2 pole 15 or 20 amp (as appropriate for the wire size) GFCI breaker for this circuit.
Best to have electrician do this, but you may need to ask an electrician if something like this can be done.