Praise be to Allah.
This transaction that you want to engage in includes two things:
1 – Buying a car through the bank. This is not permissible unless two conditions are met:
(i)That the car should be owned by the bank. So the bank should buy the car for itself from the showroom, before selling it to you.
(ii)That the bank should take possession of the car by moving it physically from the showroom before selling it to you.
If both or either of these two conditions are not met, then the transaction is haraam. See question no. 36408.
2 – Selling this car which has only been bought for this purpose, namely obtaining money. This is what is called tawarruq or buying and selling in order to obtain wariq, i.e., silver.
This is permissible according to the majority of scholars, subject to the condition that the car be sold to someone other than the person from whom you bought it.
It says in Fataawa al-Lajnah al-Daa’imah (13/161):
We hope that you can advise us about the issue of tuwarruq and tell us what the ruling is on that.
The Committee replied:
Tuwarruq means buying a product and deferring the payment, then selling it for payment on the spot to someone other than the person from whom you bought it for a deferred payment, in order to benefit from its price. There is nothing wrong with this transaction according to the majority of scholars.
See also question no. 45042.
If the two conditions outlined above are met, there is no sin on you in sha Allaah.
And we ask Allaah to help you and guide you.
And Allaah knows best.