If you were told how to effectively build trust through email marketing then how you would have described it in simple words?
Just create engagement, care about their well beings, talk to them every now & then, interact with casually, that's it.
You also can't create engagement without knowing the audience. How you have acquired the lists, may I ask?
Bought it from a good source. Only 10% of the list is can told as cold.
Well then start by greeting them. I am assuming that they are aware of you.