My son started having existential crises (or whatever you prefer to call them) at around 3. He started asking serious, probing questions about the nature of consciousness, what happens to consciousness when the body dies, what the nature of God-consciousness is, and so on. He also started at about that time to wrestle with the idea of "infinity" - how could the Universe be infinite? If the universe is expanding, what is it expanding into? What existed before the Big Bang? And so on.
He would have really big feelings during these sessions. I remember visiting my parents and lying on the bed with him as we both cried and he wrestled with his new idea that some day his consciousness might end and that I would die.
I found it very hard, myself, to deal with. (After all, I share many of these concerns myself!) I did my best to remain present with him and affirm that he was having really big ideas that even many adults would find quite unsettling. I also settled on a philosophical approach of just telling the truth, all the time. So I didn't say "Well, God is X and this is what happens when you die" (we don't share a family religion, which complicates things somewhat), but instead "Some people think this happens. Other people think this happens. Still other people think this happens."
This was quite hard for me and I often wished that I could just say "This is what our communal religion teaches", but after a while I realized that I was probably taking an overly rosy view of what that would be like. Because with my kid, asserting that things that are not verifiable are a certain way is a path to difficulty. We do not do Santa, in part because as a mixed-religion family it felt too complicated, and in part because literally the first time he heard about Santa, he spent about a minute intently studying the image of sled/jolly man/rooftop/gifts, then turned to me and said "This isn't true, right?" He has a brain that sees many potential holes in an argument. Unless I'm willing and able to defend - and defend well - every single hole (and with some stuff I am) I don't even start. Too hard. So I tell him what I believe about God and the afterlife, but I don't assert that it is factually correct for everyone, because his brain really needs systems to work universally or it starts finding the gaps. I am often not prepared, myself, to fill in all of the gaps so it is just not always possible for me to hand him a unified theory that works.
I think it's been helpful to talk about how our brains are like focusing mechanisms, and sometimes "sad thoughts" can have a lot of pulling power, and you can consciously switch the focus of the brain if you try and keep at it. Pondering death and consciousness can be emotionally overwhelming in very young people, so it's useful to know you can, with effort, focus yourself elsewhere. (I do my best to model this.)
It's hard. You have my sympathies! On the other hand, now that he's a bit older, this drive to find meaning is also kind of fun to watch in him. He has recently started to discuss gender roles (he has longish hair, and recently a lady with short hair told him he should cut his hair to be more appropriately boyish... you can imagine the number of long conversations about gender norms and hypocrisy and wanting to control others we had after that), adult control of what children read, social justice, etc. So I do feel like this is an area where growth has really improved things for us, as the distance between what his brain is capable of thinking, and what his mind is ready to think has become a little smaller.
