Figs bear several times a year
They have two crops per year if you are lucky, the breba crop and the main crop.
There are many varieties, and for the most part you can find figs of some kind pretty much available year round.
The past couple of hundred years has seen rapid developement of desirable qualities in most fruits, this includes pushing early and late varieties beyond what was available a few decades ago. For example, I have recently planted three cultivars, early, mid and late of one species of fruit, only one of which was available when I was a kid. For the purpose of this discussion we should stick to varieties that were available around Jerusalem 2000 years ago and not confuse the issue with modern varieties currently available in the USA.
It is perfectly reasonable to expect that there were periods when there would not be edible figs on trees with leaves, near Jerusalem, 2000 years ago.
That said, the author of the passage, claimed that it was not the season. If that is incorrect, then all of his writings are unreliable, not just this one passage.
In cursing the strangulating tree, (which represented a vampire-like structure sucking the life out of people), Jesus then took an action to make that curse public. That action was displayed by what he did when he went into Jerusalem and turned over the table of the money changers.
I have been inside a strangler fig. They are several species of plants that grow in tropical rain forests. They do not grow near Jerusalem. They could not grow near Jerusalem. They are nothing to do with Jesus zapping common fig trees in Israel.
Cheers
Chris