We humans, along with every other living thing on our planet, do have a start and an end, and all of the time spent and lived between the start and end I call "my" time line. My time line appears to me like a long stretch of railroad track that I am standing beside. I am standing in relation to the track as today and to my left, as far as I can see is my past with all of its events and happenings. To my right is my future as far as I can see, with it's events and happenings. This works for me and there are other configurations that may work better for you.
As far as the Cosmos and time the increments are so large that we humans may think of time as not existing. What we think of time is our concept of how "time" is used or not used. To borrow a quote from Star Trek "Some one told me that Time is a predator that stalks us all our lives, but I rather believe that time is a companion that goes with us on the journey, and reminds us to cherish every moment. because they will never come again. what we leave behind is not as important as how we have lived". How we have utilized our time. Our world is about perceptions and time can't be changed, however our perceptions of time, can be. "Time" Robert