This is from an excellent timeline by Andrew Timme (https://dribbble.com/shots/15410048-Tenet-Timeline) and shows how the story plays out.
I've highlighted the section from the perspective of the future civilisation where the alogrithm is created.
That gives loads of options for either a limited series like Dark or a prequel movie.
Against a backdrop of catastrophic climate change, a scientist discovers the algorithm and creates the inversion machines. Those in power realise that this might offer a future in an Earth where the climate improves, albeit a a risk of destroying the Earth anyway either through annihilation (which we never see) or grandfather paradoxes.
Then we have a period where the baddies learn to do battle backwards, and start a war to control the machines. The war is mentioned, and there's a vast collection of "detritus" in a dedicated research institute.
Then there's the work to bury the artefacts in the past, which presumably must be multi-generational, and offer lots of scope for interesting interactions.