The Conceptual Nature of Salvation by the Cross

Salvation through Christ's death on the cross sounds wonderful. It sure beats fulfilling every OT commandment as a means to salvation. However, I am frequently mystified by the concept of being saved by Christ's death on the cross. It seems to be a conceptual reality similar to a thought experiment. One is basing an entire system of salvation and its related lifestyle and experience to an event that not one of us can empirically prove.

Additionally, it's odd, for want of a better word,  that the God who said thou shall not also died to solve the "problem " of his creatures violating the "thou shall nots". No wonder Paul says that to the Greeks the Gospel seemed like foolishness.
With science daily redefining what reality is or might be, thanks to the unfolding of String Theory, dark energy, the Multiverse and the hint of parallel worlds, all inferred by the mathematics itself, it sometimes befuddles the mind to speak of the historical act of redemption as the quintessential conceptual and theological Theory.
Nevertheless, for whatever psychological and philosophical comfort it provides, I cannot abandon my faith, however tenuous or conceptual it has become. I've seen the  practical and transformative value of  the Cross in my life and in that of  others.