diff --git a/yt_dlp/extractor/youtube/_video.py b/yt_dlp/extractor/youtube/_video.py
index ff74195649..48e599e430 100644
--- a/yt_dlp/extractor/youtube/_video.py
+++ b/yt_dlp/extractor/youtube/_video.py
@@ -79,6 +79,7 @@ STREAMING_DATA_FETCH_GVS_PO_TOKEN = '__yt_dlp_fetch_gvs_po_token'
 STREAMING_DATA_PLAYER_TOKEN_PROVIDED = '__yt_dlp_player_token_provided'
 STREAMING_DATA_INNERTUBE_CONTEXT = '__yt_dlp_innertube_context'
 STREAMING_DATA_IS_PREMIUM_SUBSCRIBER = '__yt_dlp_is_premium_subscriber'
+STREAMING_DATA_FETCHED_TIMESTAMP = '__yt_dlp_fetched_timestamp'
 
 PO_TOKEN_GUIDE_URL = 'https://github.com/yt-dlp/yt-dlp/wiki/PO-Token-Guide'
 
@@ -3244,6 +3245,7 @@ class YoutubeIE(YoutubeBaseInfoExtractor):
             elif pr:
                 # Save client details for introspection later
                 innertube_context = traverse_obj(player_ytcfg or self._get_default_ytcfg(client), 'INNERTUBE_CONTEXT')
+                fetched_timestamp = int(time.time())
                 sd = pr.setdefault('streamingData', {})
                 sd[STREAMING_DATA_CLIENT_NAME] = client
                 sd[STREAMING_DATA_FETCH_GVS_PO_TOKEN] = fetch_gvs_po_token_func
@@ -3256,6 +3258,7 @@ class YoutubeIE(YoutubeBaseInfoExtractor):
                     f[STREAMING_DATA_FETCH_GVS_PO_TOKEN] = fetch_gvs_po_token_func
                     f[STREAMING_DATA_IS_PREMIUM_SUBSCRIBER] = is_premium_subscriber
                     f[STREAMING_DATA_PLAYER_TOKEN_PROVIDED] = bool(player_po_token)
+                    f[STREAMING_DATA_FETCHED_TIMESTAMP] = fetched_timestamp
                 if deprioritize_pr:
                     deprioritized_prs.append(pr)
                 else:
@@ -3372,8 +3375,12 @@ class YoutubeIE(YoutubeBaseInfoExtractor):
         # save pots per client to avoid fetching again
         gvs_pots = {}
 
+        # For handling potential pre-playback required waiting period
+        playback_wait = int_or_none(self._configuration_arg('playback_wait', [None])[0], default=6)
+
         for fmt in streaming_formats:
             client_name = fmt[STREAMING_DATA_CLIENT_NAME]
+            available_at = fmt[STREAMING_DATA_FETCHED_TIMESTAMP] + playback_wait
             if fmt.get('targetDurationSec'):
                 continue
 
@@ -3555,6 +3562,10 @@ class YoutubeIE(YoutubeBaseInfoExtractor):
             if single_stream and dct.get('ext'):
                 dct['container'] = dct['ext'] + '_dash'
 
+            # For handling potential pre-playback required waiting period
+            if live_status not in ('is_live', 'post_live'):
+                dct['available_at'] = available_at
+
             if (all_formats or 'dashy' in format_types) and dct['filesize']:
                 yield {
                     **dct,
@@ -3592,6 +3603,10 @@ class YoutubeIE(YoutubeBaseInfoExtractor):
             if not all_formats and key in itags[itag]:
                 return False
 
+            # For handling potential pre-playback required waiting period
+            if live_status not in ('is_live', 'post_live'):
+                f['available_at'] = available_at
+
             if f.get('source_preference') is None:
                 f['source_preference'] = -1
 
@@ -4037,12 +4052,6 @@ class YoutubeIE(YoutubeBaseInfoExtractor):
         if needs_live_processing:
             self._prepare_live_from_start_formats(
                 formats, video_id, live_start_time, url, webpage_url, smuggled_data, live_status == 'is_live')
-        elif live_status != 'is_live':
-            # Handle pre-playback waiting period
-            playback_wait = int_or_none(self._configuration_arg('playback_wait', [None])[0], default=6)
-            available_at = int(time.time()) + playback_wait
-            for fmt in formats:
-                fmt['available_at'] = available_at
 
         formats.extend(self._extract_storyboard(player_responses, duration))