How were the Americans able to get the United Nations involved in the Korean War, even over the USSR's veto in the Security Council?

Boycott by the Soviet Representative

Explanation:

Months prior to the vote regarding the invasion of South Korea by North Korea, the Soviet representative at the UN Security Council, Jacob Malik, had been instructed by Stalin to boycott further votes after the Soviet proposal to expel Nationalist China from the council in favor of installing the People's Republic (Mainland) of China as the rightful permanent member. With the USSR not having a representative when the issue of the Norh Korean invasion came up, the resolution in favor of intervention failed to have a veto vote from the Soviets.