You cannot. That's not what AL is for
The problem is that you are not hitting the right format. Adventurers League (AL) and other organized play (OP) are not meant to replace your home campaign. They are an avenue to play more and meet new and different people than your regular group.
I assume that you are talking about playing the adventure books, such as Storm King's Thunder, Curse of Strahd and the like. When run and played within the confines of AL, what you want is not really possible. Heck, I don't know many adventurers who live in Barovia for too long without simply turning into a local...
The thing I found in most OP is that time is relatively irrelevant. You travel from point A to point B "off-camera".
I run and operate the Legacies OP campaign (FOELegacies.com) and I move time forward through a series of methods:
I write adventures that follow each other, time-wise. Adventure 1–2 are in the spring, 3–5 in the summer and 6–8 in the fall and winter (I have few winter adventures).
The setting advances with the time and season. So children are born, marriages made and broken, wars started, etc.
Legacies takes these things into account. However, Adventurers League is not concerned with those things. They have seasons and I find the word very appropriate.
So, to answer your question, I do not think it is possible, as a pure AL game, to do what you want. There is no need for it.
AL, Pathfinder Society (PFS) and even Legacies are not home games where you can worry about whatever detail you like. Would it be great if they did? Perhaps. However, the format of "play anytime, join when you can" does not lend itself to a linear time-determined game.