Can science explain the origin of life without God?

No - not as things stand: science has no agreed mechanism for how the first living, self-replicating cell arose, and researchers themselves describe the problem as open. That is not for lack of careful work; real progress has been made on sub-problems. The famous Miller-Urey experiment showed that some of life's building blocks, like amino acids, can form spontaneously - a genuine landmark. But it produced building blocks, not living systems, and certainly not the thing that has come to dominate the field: the origin of biological information, the coded instructions in the first self-replicating cell. And its assumed early atmosphere is now widely thought not to match the real early Earth.

That opening is where a design inference enters - but it must be stated with care. The strongest version is not "science can't explain it, therefore God," which would be an argument from ignorance. It is an inference to the best explanation: in every other case we know, coded information traces back to a mind, so a mind is a serious candidate for the information in the first cell. This inference is contested and defeasible, not a proof. Absence of a current natural explanation is not proof that none exists; anyone who says abiogenesis is impossible has overreached.

One thing worth stressing: this question is not about evolution. The origin of life (abiogenesis) and the origin of species (evolution) are distinct problems - Darwin himself set the first aside. The design inference here concerns only the first cell, and it does not require rejecting common descent or evolutionary biology, on which sincere Christians hold a range of views. So science has not closed this question, and a mind remains a reasonable candidate among rivals - offered as an honest inference, not a knockdown proof.