diff --git a/airflow/providers/google/common/hooks/base_google.py b/airflow/providers/google/common/hooks/base_google.py
index a149831cab5..0e2c6b17ad5 100644
--- a/airflow/providers/google/common/hooks/base_google.py
+++ b/airflow/providers/google/common/hooks/base_google.py
@@ -515,9 +515,6 @@ def provide_authorized_gcloud(self):
                         f"--key-file={os.environ[CREDENTIALS]}",
                     ]
                 )
-            if project_id:
-                # Don't display stdout/stderr for security reason
-                check_output(["gcloud", "config", "set", "core/project", project_id])
             elif os.path.exists(credentials_path):
                 # If we are logged in by `gcloud auth application-default` then we need to log in manually.
                 # This will make the `gcloud auth application-default` and `gcloud auth` credentials equals.
@@ -539,6 +536,11 @@ def provide_authorized_gcloud(self):
                             creds_content["refresh_token"],
                         ]
                     )
+
+            if project_id:
+                # Don't display stdout/stderr for security reason
+                check_output(["gcloud", "config", "set", "core/project", project_id])
+
             yield
 
     @staticmethod
diff --git a/tests/providers/google/common/hooks/test_base_google.py b/tests/providers/google/common/hooks/test_base_google.py
index fd4cd613bb3..93b3b2d2bfd 100644
--- a/tests/providers/google/common/hooks/test_base_google.py
+++ b/tests/providers/google/common/hooks/test_base_google.py
@@ -742,12 +742,12 @@ def test_provide_authorized_gcloud_via_gcloud_application_default(
                 # Do nothing
                 pass
 
-        mock_check_output.has_calls(
+        mock_check_output.assert_has_calls(
             [
                 mock.call(['gcloud', 'config', 'set', 'auth/client_id', 'CLIENT_ID']),
                 mock.call(['gcloud', 'config', 'set', 'auth/client_secret', 'CLIENT_SECRET']),
-                mock.call(['gcloud', 'config', 'set', 'core/project', 'PROJECT_ID']),
                 mock.call(['gcloud', 'auth', 'activate-refresh-token', 'CLIENT_ID', 'REFRESH_TOKEN']),
+                mock.call(['gcloud', 'config', 'set', 'core/project', 'PROJECT_ID']),
             ],
             any_order=False,
         )