I think I pinpointed an approximate date.
Near the beginning of the first episode, Alex is playing the first Star Wars Battlefront game, which came out in November 2015. In several lines of dialogue, Amy is said to have disappeared "two years ago". If the game's loading screen is anything to go by, she had to have disappeared exactly two years or more after that game was released. It can't be less than that based on the game's "day/week/month/year" date estimation system (ex. 7 weeks ago, 8 months ago, etc.)
So I would guess around
November 2017; especially if that Thanksgiving scene ends up in the show given the context that the Pride approached them during the feast.
Here's the screenshot of Alex's TV: