If the universe is to ever be understood, then would our actions not be seen if someone could rewind it and play it back?
Or would our entire existence contribute nothing more than noise compared to routinely occurring grandiose events?
In the grand scheme of things, no. Eventually our sun will run out of fuel to burn and humanity will be frozen to death, if we haven’t killed ourselves in a nuclear holocaust before that.
Even on a lesser scale, the vast majority of people are completely forgetten 100 years after their deaths.
Our actions may be forgotten, but it will always be the case that we have performed them.
It’s not that our actions are “nothing more than noise,” it’s that the noise will eventually drown out all of our actions.
What he said.
However, discernability doesn’t necessarily mean that they didn’t occur and don’t continue to ripple like a stone in a pond.
Since every action results in a reaction and it all comes down to energy and the exchanges thereof, yes, our actions exist forever.
Would someone “rewinding” SEE or be able to differentiate our individual actions from the total? Likely not. But what they DID see would be the result, at least in part, of our actions.
It’s a crappy sort of immortality, but it IS immortality in a sense. 
Isn’t this the same question as asking if the past ‘exists’?
There’s always the Collective Subconscious, as theorized by psychologist Carl Jung.
It’s currently unknown how to “tap into” this supposed unconsciousness, however. Maybe the the iPhone’s next version will contain that feature…
Chaos theory implies that even the smallest of our actions will compound with time to alter the world in large ways eventually. However, these effects are effectively random and bear little semantic relation to the causes.
From the perspective of most western religions, people’s souls are eternal. So not only do yoru actions have an eternal impact on your own self, but you can have lasting impact on everyone you interact with.
I realize this is not really what you are looking for, but it is another perspective.