I find that a lot of the common answers to divine hiddenness only work given a non Calvinist view of free will.
Do you mean that they take the view that for God's presence to be too clear would take away our freedom in response to him? e.g. CS Lewis in some of his writings? In which case, yes, that does seem problematic.
How would you guys go about responding to the problem. I think I have a solid answer, I'm just curious what others thoughts are
Sin! Romans 1:18 has to be at the heart of our answer - though, as verse 20 says, God's power and divine nature are clearly seen, we suppress the truth. In debate, people often are reluctant to press this - e.g. against people like Alex O'Connor, who pushes the divine hiddenness argument strongly. But his arguments. and those of a lot of modern philosophers pushing this argument centre (as I understand it) on the existence of non-resistant non-belief: people who aren't against belief in God but would believe if he made himself clearly present to them.
But any Christian answer has to immediately deny that there has ever been anyone in this situation. We
all resist, though in very different ways. To argue that strongly and convincingly would mean to demonstrate sin and the way in which it causes us to deny evident truths and push them into our subconscious.
There may also be space for talking, about what it would
mean for a transcendent God to be apparent - 'in him we live and move and have our being', after all... Creation is awesome, but we take it for granted; conscience speaks without ceasing in our lives (thus moral arguments for God) but we think it's just part of being human, or dismiss it as an artifact of evolution, or whatever. A genuinely transcendent God is present, but not necessarily so easy to recognise - as the fish may struggle to recognise water. This mustn't be argued in a way to make it an excuse, which it isn't. But it does offer space to ask - what are you looking for, when you look for evidence of God?
CS Lewis's argument that Jesus' miracles in a sense underline and point to the fact that God does these things
all the time is helpful here - he turns water into wine every year with grapes, he heals the sick every day, but we just don't notice until Jesus comes along and does it in a more unusual way.
And I suspect that's the experience a lot of us have when we become Christians: we suddenly look about us and see a world suffused with the glory and presence of god, not because the world has changed, but because our eyes have been opened.