1. The so-called "law of biogenesis" came from the refutation of an outdated idea about the origin of life: that outdated idea is called spontaneous generation.
Spontaneous generation held that organisms - even those as complex as flies, rats, and frogs - could just spontaneously arise in a few days or weeks, and that complex life arising goes on all the time, all around us, under all kinds of conditions, throughout history. Several scientists started chipping away at that notion and Loius Pasteur drove the final nail in the coffin of spontaneous generation.
The modern view of the origin of life is abiogenesis, not spontaneous generation. In abiogensis, the first life would have been far far far far far far far far far far simpler than the simplest prokaryote alive today, would have taken possibly tens of millions of years to arise, would have arisen only once, and would have involved conditions unlike those present on today's earth. The experiments that refuted spontaneous generation don't even touch abiogenesis.
So no, the "law of biogenesis" does not refute abiogenesis.
2. It is a misnomer to speak of a scientific law of biogenesis. The closest thing to it is the part of the cell theory which states that all cells arise from preexisting cells. But then that is nothing more than an inductive conclusion: every cell we've even seen arise arose from a preexisting cell, so it is inductively concluded that that applies to all cells. But, there is no logical requirement that it apply to all cells: it's an extrapolation. There are untold numbers of similar inductive conclusions that were later proven false in science. For example, for decades biologists had not found any prokaryote that had a cytoskeleton so it was taught that no prokaryotes have a cytoskeleon: but then we found some prokaryotes that do have a cytoskeleton.
So no, one cannot prove the existence of a creator with the so-called "law of biogenesis."
PS: Besides, the Creator would be astronomically greater than the first living organism, right? So it would be more logical to accept that life just existed without a cause than it would be to accept that a Creator just existed without a cause. Calling upon a Creator does not solve anything: it just makes things worse. It replaces one mystery with an every bigger one.