Here is something I wrote a while ago, but I think it applies.
I don't see how God's grace can be anything but unconditional, including not depending upon the condition of 'belief.' I think of grace in this life as healing the brokenness we experience when we feel separated from God and each other, and from ourselves. The healing grace is pouring freely down on all of us at all times in this life but unless we open the cups of our hearts to it, we can't drink.
O Son of Being! Love Me that I may love thee. If thou lovest Me not, My love can in no wise reach thee. Know this, O servant. (Baha'i Hidden Word)
Come near to God and he will come near to you. (James 4:8)
Opening up to that love is like channeling water into an irrigation system, rather than letting it pour out on the ground.
That's this life, and salvation is for now. In this life we rebel, we blame, we shame, we consistently fall short of the goodness we were created for. Grace is not an excuse for this, but the remedy. Grace is not static: it must flow to do its work. We receive God's grace and in turn give it to others, and to ourselves. Forgiveness, love, healing. These are the qualities of grace. And still we fall short.
In this life we can step into the river of God's grace, or we can stand on the bank saying who needs that silly old river anyway. The river is unconditionally there, it's our choice to step in or not.
But I think this question is about something else as well: unconditional grace with respect to what happens in the next life. Our human ideas of good and evil, of justice, are offended by the idea that everyone 'gets in free.' But God made us all and like Origen I can't reconcile a loving Creator with a god who would send any of his creatures to eternal torment, fully knowing how fragile we are in mind, body, and spirit. I have my own ideas and metaphors about what might happen in the next life, perhaps the closest idea being that we are drops that merge with God's Ocean yet somehow in a way that allows the love we've cultivated here to persist eternally. I believe in a final judgement, one in which the fire of the Holy Spirit burns away any part of us that is not love, like refining gold in a crucible. I believe in (trust in) God's justice, but I can't fathom it because my hope lies in the idea that it is a justice with no trace of revenge, and a justice that takes all of our fragility and complexity and brokenness into consideration. It is a justice beyond human imagination, so I don't even try.
The language of the Bible is metaphore and parable; we know very little about the next life beyond our assurance that it exists. Every mention of heaven and hell in the Bible can be understood as Jesus telling us about how to conduct ourselves in this life, for creating heaven or hell here and now on earth, rather than about separating sheep and goats in the next life. I'd sooner believe in reincarnation than I would in an eternal torment, but instead I believe the Bible that everything will end up in God, all in all (1 Cor 15:28).