diff --git a/test_runner/fixtures/safekeeper/http.py b/test_runner/fixtures/safekeeper/http.py
index 96c84d1616..7f170eeea3 100644
--- a/test_runner/fixtures/safekeeper/http.py
+++ b/test_runner/fixtures/safekeeper/http.py
@@ -8,6 +8,7 @@ import requests
 from fixtures.common_types import Lsn, TenantId, TenantTimelineId, TimelineId
 from fixtures.log_helper import log
 from fixtures.metrics import Metrics, MetricsGetter, parse_metrics
+from fixtures.utils import wait_until
 
 
 # Walreceiver as returned by sk's timeline status endpoint.
@@ -161,6 +162,16 @@ class SafekeeperHttpClient(requests.Session, MetricsGetter):
             walreceivers=walreceivers,
         )
 
+    # Get timeline_start_lsn, waiting until it's nonzero. It is a way to ensure
+    # that the timeline is fully initialized at the safekeeper.
+    def get_non_zero_timeline_start_lsn(self, tenant_id: TenantId, timeline_id: TimelineId) -> Lsn:
+        def timeline_start_lsn_non_zero() -> Lsn:
+            s = self.timeline_status(tenant_id, timeline_id).timeline_start_lsn
+            assert s > Lsn(0)
+            return s
+
+        return wait_until(30, 1, timeline_start_lsn_non_zero)
+
     def get_commit_lsn(self, tenant_id: TenantId, timeline_id: TimelineId) -> Lsn:
         return self.timeline_status(tenant_id, timeline_id).commit_lsn
 
diff --git a/test_runner/regress/test_wal_acceptor.py b/test_runner/regress/test_wal_acceptor.py
index 8ee548bdb0..adfe292c24 100644
--- a/test_runner/regress/test_wal_acceptor.py
+++ b/test_runner/regress/test_wal_acceptor.py
@@ -2084,8 +2084,13 @@ def test_timeline_copy(neon_env_builder: NeonEnvBuilder, insert_rows: int):
 
     endpoint.safe_psql("create table t(key int, value text)")
 
-    timeline_status = env.safekeepers[0].http_client().timeline_status(tenant_id, timeline_id)
-    timeline_start_lsn = timeline_status.timeline_start_lsn
+    # Note: currently timelines on sks are created by compute and commit of
+    # transaction above is finished when 2/3 sks received it, so there is a
+    # small chance that timeline on this sk is not created/initialized yet,
+    # hence the usage of waiting function to prevent flakiness.
+    timeline_start_lsn = (
+        env.safekeepers[0].http_client().get_non_zero_timeline_start_lsn(tenant_id, timeline_id)
+    )
     log.info(f"Timeline start LSN: {timeline_start_lsn}")
 
     current_percent = 0.0