But I would be cautious calling a billion years or so "shortly" even in the context of a four-something billion year old planet. A billion is a very big number, especially when you multiply it by how many trillions of little potential multi-dimensional petri dish situations were around for each second of each year of those billion years.

And it could have happened only once because once established, it tends, on a timescale orders of magnitude shorter than a billion years, to squelch the appearance of other forms, at a minimum by guiding them along with its template, or alternatively by smothering them.

But this all says nothing about whether it happened on Earth or elsewhere. Either one could still be true.