What would it take to “officially” designate Golden Gate Park a historic landmark?  The process begins at the state level;  historic landmarks must be registered by a state first and then they may be considered for national historic landmark designation (a process managed by the National Park Service).  In California the Office of Historic Preservation is under California State Parks.  Here is a summary of that program:

“The State Historical Resources Commission has designed this program for use by state and local agencies, private groups and citizens to identify, evaluate, register and protect California’s historical resources. The Register is the authoritative guide to the state’s significant historical and archeological resources.

The California Register program encourages public recognition and protection of resources of architectural, historical, archeological and cultural significance, identifies historical resources for state and local planning purposes, determines eligibility for state historic preservation grant funding and affords certain protections under the California Environmental Quality Act.

Criteria for Designation

Associated with events that have made a significant contribution to the broad patterns of local or regional history or the cultural heritage of California or the United States (Criterion 1).

Associated with the lives of persons important to local, California or national history (Criterion 2).

Embodies the distinctive characteristics of a type, period, region or method of construction or represents the work of a master or possesses high artistic values (Criterion 3).

Has yielded, or has the potential to yield, information important to the prehistory or history of the local area, California or the nation (Criterion 4).”

via California Register.