Hm… Well, I think the Biblical record shows that people can (and were) convicted of their sin in various ways before being convicted about God’s love (as/in Christ or otherwise). Lewis certainly believed that a person has to recognize first that they need saving before they will care much about the saving love of God, and I think there’s a lot to that. People can have a shallow notion of the love of God, such that they can’t conceive of God being concerned with ‘sin’ at all.
Metaphysically, I would argue for God’s existence, God’s essential interpersonal union (and thus His existence as love), God’s relation (including love) for creation (including myself), before getting to ethics and sin (and so to the topic of God’s salvation of sinners from sin). But historically, it is a lot easier to get people to acknowledge injustice, even in themselves, than to acknowledge God’s existence, love and salvation.
(This is easily illustrated by the observation that people of practically every belief in all human history accept the reality of injustice–at least against themselves!–even if they don’t believe in God, or that God cares about such things.)