There are no guarantees that she will ever go broody.
Some breeds/varieties/strains will go broody at the drop of a hat while others seldom do. When it comes to specific individual birds you'll just have to wait and see.
Generally speaking she's more likely to broody in the spring though some will do it anytime. Usually after she's sized her eggs up to their full size.
If you want her to set give her a cozy, snug, dark nest with good airflow and not too much excitement around her and let a few eggs accumulate (mark them) in the nest. That may help her get into the mood, but there are no guarantees.
I had hatchery hens for over a year and 1/2 and none went broody but when I got heritage types from breeders they are brooders for sure. Sexlinks and hatchery hens are mostly for laying and the broodiness has been almost bred out of them. Gloria jean