Destiny is set where the Traveler arrived in 2014, when the game was released. Now in the City Age, the question is: what is the current year? Using the information from grimoire cards and in-game sources, let’s try and get a rough estimate.
In the card Ghost Fragment: Human, there is an interview about the Ares One mission to meet the Traveler on Mars. There are no references on how long it took the Traveler to terraform Jupiter, Mercury, and Venus, but we do know it took fourteen months for the crew to fly to Mars. After they meet the Traveler, fifty years pass and the interview with Captain Jacob happens. Let’s assume the Golden Age took two centuries. I could take them long for technology to advance for Warminds, like Rasputin, to have weapons that could damage the Traveler. This would make the year 2216, with a two-year time frame for the Ares One rocket to be built and its ride to Mars.
If the Golden Age lasted for two centuries, then the Collapse happened during 2216. The Darkness came and the Traveler stopped its destruction. To find out a possible timeline for how long the Dark Age lasted, let’s look at a real-life version of coming back in technology: The Middle Ages. It was caused by the fall of the West Roman Empire, which created a void in Europe. It took 500 years for the area to rise from the “Dark Age” of the Middle Ages. Afterwards, technology slowly began again and trade routed opened. With the information about a real life Dark Age, we can assume that it took just as long for us in Destiny to start the City Age. This would make the year 2716.
Now at the City Age. The Crucible wasn’t around in the form we know until the sometime after the City Age began. In the card, Ghost Fragment: Cayde-6, he is looking up events from 126 years ago. One of the minor events was Ikora’s 25-win streak, back in her Crucible days. The card was from the Age of Triumph, which would a year ago in game. So, if we add 127 years to the date, the present year would be 2843.
Another way to look at the timeline would be to add era dates. Today we have BCE, and CE. So, if we make the Collapse as the beginning of AC, or After Collapse, then the year would be 726 AC.
P.S. – There are a lot of assumptions here, with all the uncertainties, it is hard to find a specific date for the Destiny timeline. There is a lot missing from the world, and most of the events have no dates, or references to when other events happened with each other. This is just my view of the timeline with a bare minimum possibility.