While Tesla is already a very large automobile company based on market capitalisation, a lot of that market capitalisation is based on expectations of the future. As of the writing of this question, Tesla is losing money and selling significantly less cars than even the 20th largest auto-company in the world. Yet, the expectations that have been set for Tesla by Elon Musk would probably require Tesla to sell more cars than any other company on the planet while maintaining large profit-margins.

In order to ramp-up production from approx. 100,000 to 500,000 or 1,000,000 cars a year, Tesla has created the Model 3, its first mass market car. Regrettably, Tesla has had trouble producing the Model 3 and production of the car can be tracked here. It is likely that Tesla's total vehicle production must exceed 10 million in order for it to become the world's largest car company. Yet, given its financial situation, there is a risk that the company goes bankrupt before that happens.