I want to comment on that that Roger Penrose is considering the existence and possible detection of a universe before the big bang, something he also touched on in his Nobel lecture.
That would lead me to speculate that if we were looking for messages from the previous universe (in the style of the movie/book Contact) then we should look to the signature of the background radiation (CMB). Imagine a previous universe left us instructions there to help us achieve this, and perhaps therefore to achieve some objective that spans multiple universes (i.e. some objective too large to complete within the lifespan of a single universe).
If that isn't a sci-fi book then it should be. Also maybe an interesting area for legit academic study (e.g. how to imprint instructions in the CMB to pass along to future universes).
That was the premise behind the Stargate Universe TV series.
<spoilers> The Ancients detect a pattern in the cosmic background radiation that hints at an intelligence that existed before the beginning of time and send a fleet of automated ships with FTL to research it. Millions of years later, the US Air Force manages to send a team on a one way trip to the flagship and hijinks ensue.</spoilers>
I wonder if they were going towards a purposeful communication plot as well, or even a plot suggesting a recurrence theme. I think of it sometimes like the ouroboros/eternal-return mystical philosophy. Like, the advanced life that we end up creating in this universe knows that the only way it can recreate itself is to recreate us, like we are just some kind of bootstrap for the universe's final form.
https://chat.openai.com/share/3143a927-a283-4abd-aae3-1f0542...
So as of now, this theory is not supported by anything.
Also, even if life did not causally begin in this universe through "external" influence like this, transmitted signals may potentially influence the future of life greatly nonetheless.
―Friedrich Nietzsche