If, as you say, the effect is non-different from the cause, then for that reason the effect too must be birthless. There is no example to support the claim that the effect comes to be from an birthless cause. If the cause is produced from the result, it is not a real cause. Non-Becoming being universally emphasised by the enlightened. The absence of knowledge of antecedent and consequence itself is a signal of Non-Becoming.
Nothing whatsoever comes to be whether from itself or from another.
Nothing whatsoever real, unreal or both real and unreal comes to be. The cause does come to be from the birthless, nor indeed an effect of its own nature. Information has a cause, otherwise neither exists. From the observation of suffering dependent existence becomes credible. From a logical point of view, information requires causality.