If the breed is prone to broodiness, which in case this may not be, then season is not a major factor controlling when a hen does become broody. My hens appear to have some internal sensor that tracts reserves needed to make eggs. When reserves depleted the hen switches from egg laying to broodiness. For me a hen with limited access to feed will go broody quicker once she is in lay. My limited experience with breeds with weak inclination for broodiness indicates they do have a seasonal tendency but it is not a strict rule. Younger females, even of the broody prone breeds, may lay more eggs before going broody as they may have capacity for an alternative reproductive strategy where they cuckold other hens.
OP. consider getting something like a silkie hen if you want out of season broodiness. When she commits then swap out her eggs for eggs you want hatched.
OP. consider getting something like a silkie hen if you want out of season broodiness. When she commits then swap out her eggs for eggs you want hatched.