The first philosopher to explicitly state this view of time was Heraclitus. He said for example 'you never step into the same river twice' - because everything that exists is always being destroyed. Burnt Norton begins with two quotes from Heraclitus.
Though the logos is common to all, most people live as if they had a wisdom of their own possession
Only fragments of Heraclitus remain. He saw the whole Universe as a place of creative destruction and warfare, of which we are all components. Also, alas, in common with Eliot, he thought the mass of people were inferior and unable to grasp the nature of reality.
Here is another quote from Heraclitus, not used by Eliot:
The one is made up of all things, and all things issue from the one.
Ironically Heraclitus is a thinker who has almost disappeared, only the slightest traces of him remain in the present, burnt up by the very processes he describes.
And his thought was about the identity of destruction and creation.
But it always was, is, and will be: an ever-living Fire, partly coming to flame, and partly going out.
So, Eliot used the two quotes I have bolded above, rather than the ones I have italicised. I think the ones he chose are about ways of responding to the problem of time, rather than descriptions of the state of the Universe. And so, most of Burnt Norton is about how to live in time. The two methods recommended by Heraclitus in the two quotes are to give up one's separation from The Logos, and to take the low route in order to ascend. This is the motion of Burnt Norton.
However, I think there are two problems. One is that Heraclitus and Eliot are quite elitist, so while they talk about submerging the self, they recoil from the masses. The other is that there is a divergence between them: Heraclitus does not conceive of a god or Logos standing aloof from the universe, so his view of joining with the Logos is not as much about renouncing the world as Eliot's is.
ETA - incidentally the statement 'the logos is common to all but people act under their own wisdom' is almost a translation of the first line of the Dao De Jing: 'the way that can be followed is not the chang way' where 'chang' means 'common to all'. I often wonder whether these ideas were in some way communicated, for example by traders, or arose spontaneously in many places.