diff --git a/airbyte_cdk/sources/declarative/incremental/concurrent_partition_cursor.py b/airbyte_cdk/sources/declarative/incremental/concurrent_partition_cursor.py
index b71890cce..730f8763d 100644
--- a/airbyte_cdk/sources/declarative/incremental/concurrent_partition_cursor.py
+++ b/airbyte_cdk/sources/declarative/incremental/concurrent_partition_cursor.py
@@ -264,7 +264,10 @@ def _set_initial_state(self, stream_state: StreamState) -> None:
         if not stream_state:
             return
 
-        if self._PERPARTITION_STATE_KEY not in stream_state:
+        if (
+            self._PERPARTITION_STATE_KEY not in stream_state
+            and self._GLOBAL_STATE_KEY not in stream_state
+        ):
             # We assume that `stream_state` is in a global format that can be applied to all partitions.
             # Example: {"global_state_format_key": "global_state_format_value"}
             self._global_cursor = deepcopy(stream_state)
@@ -273,7 +276,7 @@ def _set_initial_state(self, stream_state: StreamState) -> None:
         else:
             self._lookback_window = int(stream_state.get("lookback_window", 0))
 
-            for state in stream_state[self._PERPARTITION_STATE_KEY]:
+            for state in stream_state.get(self._PERPARTITION_STATE_KEY, []):
                 self._cursor_per_partition[self._to_partition_key(state["partition"])] = (
                     self._create_cursor(state["cursor"])
                 )