You cannot make soap without sodium hydroxide.
Sodium hydroxide, also known as lye and caustic soda, is an inorganic compound with the formula NaOH. It is a white solid ionic compound consisting of sodium cations Na⁺ and hydroxide anions OH−
“At room temperature, sodium hydroxide is a white crystalline odorless solid that absorbs moisture from the air. It is a manufactured substance. When dissolved in water or neutralized with acid it liberates substantial heat, which may be sufficient to ignite combustible materials. Sodium hydroxide is very corrosive. It is generally used as a solid or a 50% solution. Other common names include caustic soda and lye. Sodium hydroxide is used to manufacture soaps” *from PubChem