If you're in Southern California, you will probably get a couple of crops, but for us up north, the 'Breba' crop is often the only one. You could prune right after picking the first crop, or you could do it a bit now. If it is a big tree and you have plenty of figs, go ahead now, but if it is a smaller tree, I'd wait till you got the first bunch of fruit.
Sounds like a big tree.
One advantage to doing it now is to force new growth down lower and get a good start on re growth.

Hi barnet,

>>> We have a Black Mission tree that was planted two years ago and that did nicely with fruit this past year.
That is great; BM is famous to do well in CA; here in NJ,(my experience), it is both a bad-twig-rooter and a late
(mature-years) fruiter.

>>> I notice there are green buds starting to appear.
SORRY, it may be a LITTLE too late to prune. Pruning
is best done on (any) DORMANT plant.

Balmy (crazy) weather in CA, may have beat you this time...
There is always a next year.

On second thoughts. Since the buds are just just just
breaking, and figs being very tolerant to pruing.
If you really really really need to prune; then do it asap,
and hope for the best.

Expect some (water/sap) weeping from the newly cut branches.