How Could LL’s Innocence Have Been Proven?

If the evidence for murdering all those babies put to LL was largely circumstantial and backed up with statistical probability, how could she have ‘potentially’ demonstrated her innocence?

What could she have theoretically said or what evidence could she have submitted during the trial to change the verdict?

She could hardly deny being on duty when she was, or that that children survived when they didn’t (apart from the ones that did).

Was the evidence so clear that she was obviously guilty before the trial even began and there was nothing she could do to avoid a guilty verdict?