Was the United Nations established immediately after World War I?

The United Nations wasn't formed after World War I; it emerged from the ashes of World War II. Think of it this way: after the First World War, the League of Nations was created in 1920 with the aim of preventing future conflicts. However, it ultimately failed to prevent the Second World War, which was far more devastating. The Second World War really highlighted the need for a stronger, more effective international organization. So, in 1945, as the war drew to a close, representatives from 50 countries met in San Francisco to establish the United Nations. The UN was designed to maintain international peace and security, develop friendly relations among nations, and promote social progress, better living standards, and human rights. So, while the idea of international cooperation existed after World War I, the specific organization we know as the United Nations is a direct result of the Second World War.
Think of a phoenix rising from the ashes 'post-Second World War', giving birth to the United Nations.