Is the purchased car permissible or forbidden, given the doubt about the proper cancellation of its sale contract to a previous buyer?

The default is that the car belongs to the company and is free from any encumbrances, and this is the default for all possessions in people's hands, which is not removed by mere doubt. Therefore, dealing with them in this matter is permissible.

As for the car having an earlier down payment, this does not cause harm, and the default is that the person who made the down payment did not complete the transaction.

However, if it is proven that the company contracted with a previous buyer for this car with a down payment that was binding on the seller, and the company sold it to you before rescinding the contract with the down payment owner: the sale is invalid, because the sale is binding on the seller alone, and the option rests with the buyer.

What is meant by the common "down payment" today, which involves paying money to reserve an item without a contract, is not intended here; that is merely a promise.

In summary, the default is that your purchase of the car is valid unless it is proven with certainty that the company sold something it did not own, or sold it before the first buyer rescinded the contract, and you are not obligated to investigate that.