I believe christians describe a situation in which the mind/heart was originally pure. But from pureness it fel into sinn one time. Buddha does not seem to teach a starting point in the past but it is more like a process of here and now.
Buddha discovered, i believe, this fall into sinn never really happened in some irrevocable or inherent way. We never became really sinners by nature, but sinn is adventitious to the pure nature of mind. Sinn is like bagage we collected over many lives and became more and more heavy, and started to feel like Me and mine.
But our mind/heart is yet still pure but only defiled by incoming adventitious defilements. It is not that we ever lost that original purity but it is overgrown, not seen anymore.
I believe this is an important teachings of the Buddha. Becoming a sinner is more like something that happens here and now. It is more like we have become more and more ignorant about our orignal pure state. What is adventitious has become during all those years more and more heavy. And while that happened it started to feel more and more like me and mine. What is really us is not heavy. Buddha did call this heaviness dukkha. Like a load. Like a burden. That’s what i believe 
So, there is a proces of blindness. Buddha teaches that all things like greed, conceit, ego, hate are rooted in this blindness. In holding things that are not me and mine as me and mine.