My over-reaching point is I think that if you start with understanding the mechanics of the various forms of birth control as well as what options are out there, paired with the kind of information you get on personal exams for you and your partner, it will be easier to tackle the other questions from a spiritual/moral standpoint.
For example, if an exam reveals your partner isn’t capable of safely carrying a pregnancy or repeated pregnancies, or you have medical issues on your side, that is information that leads to entirely different choices/needs/moral answers. If I told my doctors I was looking to go off birth control and just let God decide how often I’m pregnant, they’d flat out panic. It is not the best choice for me and my health for a whole buffet of reasons. Given that, having my husband say that he’d like to leave our birth control to God, that’s arguably not the moral, healthy, or appropriate choice. A friend of mine had a medically complex pregnancy and a traumatic delivery that resulted in a blood transfusion for the birthing parent and a month-long stay in the ICN for their child. If they elected to do quiverfull living in those circumstances and left themselves in a place to get pregnant again, it would be disastrous by just about every metric in terms of morality.
So, talk to a doctor, get checked out, get the details on birth control, how it works, the advantages and disadvantages, and get checked out. Then, once you have the science, move on to talking to your partner and a therapist and/or religious representative to find out the ethical and moral questions you have.