Create nuclear blasts that encode the information in short microbursts. Info will be available in the carbon record and in tree rings around the world .... profit?
Short story where SETI programmers turn new message hunting code on archived files and it detects a message in the human genome rather than in radio signals from the cosmos: https://www.fourmilab.ch/documents/sftriple/gpic.html
This feels like it might fit a series like The X-Files or The Outer Limits more than a full movie; there isn't much more to it than the twist; aside from that it's a story about some people.
If you don't mind them being shorts, there are some good sci-fi stories on the Dust and Omeleto channels on YouTube. e.g. this "One Minute Time Machine" - https://www.youtube.com/watch?v=vBkBS4O3yvY - has just two people, a bench, and a Time MacGuffin.
I do feel that many include space because it's fun and can be CGI modelled, or time travel because it makes for a cheap sci-fi plot, and if you rule those out you get things like The OceanMaker ( https://www.youtube.com/watch?v=uWCGK4nneeU ) which I didn't like so much because nothing really happens. Whether there are more concepty ones with more nuanced plot, they probably didn't catch my eye to watch.
You might like the "man from earth". It isn't exactly what you've described here, but it's a great movie. The entire thing takes place as a conversation amongst a group of friends where they extrapolate out on somebody's seemingly crazy assertion.
like in ST:TNG where it turns out there's a piece of code in the DNA of all the humanoid species that together form a message from the civilization that seeded them