feat: 이벤트 진행 시작될 때 자동 새로 고침

packages/user/src/pages/NotStartedEventPage.tsx

@@ -1,3 +1,4 @@
+import { useEffect, useRef } from 'react';
 import { useRouteError } from 'react-router-dom';
 import EventTimer from 'src/components/shared/timer/index.tsx';
 import useGetEventDuration from 'src/hooks/query/useGetEventDuration.ts';
@@ -6,12 +7,29 @@ import CustomError from 'src/utils/error.ts';
 
 export default function NotStartedEventPage() {
 	const error = useRouteError() as CustomError;
+	const timerRef = useRef<ReturnType<typeof setTimeout> | null>(null);
 
 	const {
 		duration: { startTime },
 		formattedDuration,
 	} = useGetEventDuration();
 
+  useEffect(() => {
+    if (error.status === 403 && startTime) {
+      const current = new Date().getTime();
+      const start = new Date(startTime).getTime();
+      const timeUntilStart = start - current;
+
+      if (timeUntilStart > 0) {
+        timerRef.current = setTimeout(() => window.location.reload(), timeUntilStart);
+      }
+    }
+
+    return () => {
+      if (timerRef.current) clearTimeout(timerRef.current);
+    };
+  }, [startTime, error.status]);
+
 	if (error.status === 403) {
 		return (
 			<div