You don’t have to trust the Bhagawad Gita if you don’t want to. If you are asking how you can bring yourself to trust what the Bhagawad Gita says, then the answer is — by exploring it’s message.
I don’t believe in the existence of God and even I find parts of the Gita sublime. But if sublimity is what you seek, then you can find it as easily in other places. In movies like Inception or Interstellar for example, which are said to have borrowed ideas from Indian philosophy.
You can also find sublime ideas in the written works of writers and scholars both contemporary and ancient. Philosophy is as old as civilisation is. The Bhagawad Gita is one of its manifestations. There are many others.
If you are asking about the historicity of the Bhagawad Gita, then there is less reason to trust it. This is because the supernatural aspects of the narrative make it implausible and also because the Mahabharata — inside which the Gita exists — seems to have been a work of literature that evolved over many years.
Of course, how a book got written says nothing about its quality. The Bhagawad Gita does not have to be spoken by Krishna to be meaningful. It’s message stands on its own just as it would if it had been composed by the sage we call Ved Vyasa or by someone else.