Here is the applicable Vehicle Code section:
21802. (a) The driver of any vehicle approaching a stop sign at the
entrance to, or within, an intersection shall stop as required by
Section 22450. The driver shall then yield the right-of-way to any
vehicles which have approached from another highway, or which are
approaching so closely as to constitute an immediate hazard, and
shall continue to yield the right-of-way to those vehicles until he
or she can proceed with reasonable safety.
(b) A driver having yielded as prescribed in subdivision (a) may
proceed to enter the intersection, and the drivers of all other
approaching vehicles shall yield the right-of-way to the vehicle
entering or crossing the intersection.
(c) This section does not apply where stop signs are erected upon
all approaches to an intersection.
It is an arguable presumption that you failed to yield until it was safe to cross.
Absent a police report, this will be an issue for the two insurance companies to hash out. Even if there IS a police report, the insurers can still apply fault in whatever measure they feel is appropriate. The insurers can divide fault between the two parties, the police report cannot.
Speed and visibility might play a factor, but if these were straight roadways absent any hills or sharp turns at high speed that would have obstructed your view of oncoming traffic, you may be fighting an uphill battle to argue that the approaching driver shared fault.