diff --git a/openmp/libomptarget/DeviceRTL/include/Mapping.h b/openmp/libomptarget/DeviceRTL/include/Mapping.h
--- a/openmp/libomptarget/DeviceRTL/include/Mapping.h
+++ b/openmp/libomptarget/DeviceRTL/include/Mapping.h
@@ -34,9 +34,19 @@
 bool isGenericMode();
 
 /// Return true if the executing thread is the main thread in generic mode.
+/// These functions will lookup state and it is required that that is OK for the
+/// thread and location. See also `isInitialThreadInLevel0` for a stateless
+/// alternative for certain situations, e.g. during initialization.
 bool isMainThreadInGenericMode();
 bool isMainThreadInGenericMode(bool IsSPMD);
 
+/// Return true if this thread is the initial thread in parallel level 0.
+///
+/// The thread for which this returns true should be used for single threaded
+/// initialization tasks. We pick a special thread to ensure there are no
+/// races between the initialization and the first read of initialized state.
+bool isInitialThreadInLevel0(bool IsSPMD);
+
 /// Return true if the executing thread has the lowest Id of the active threads
 /// in the warp.
 bool isLeaderInWarp();
diff --git a/openmp/libomptarget/DeviceRTL/src/Kernel.cpp b/openmp/libomptarget/DeviceRTL/src/Kernel.cpp
--- a/openmp/libomptarget/DeviceRTL/src/Kernel.cpp
+++ b/openmp/libomptarget/DeviceRTL/src/Kernel.cpp
@@ -83,7 +83,7 @@
     return -1;
   }
 
-  if (mapping::isMainThreadInGenericMode(IsSPMD))
+  if (mapping::isInitialThreadInLevel0(IsSPMD))
     return -1;
 
   if (UseGenericStateMachine)
diff --git a/openmp/libomptarget/DeviceRTL/src/Mapping.cpp b/openmp/libomptarget/DeviceRTL/src/Mapping.cpp
--- a/openmp/libomptarget/DeviceRTL/src/Mapping.cpp
+++ b/openmp/libomptarget/DeviceRTL/src/Mapping.cpp
@@ -164,20 +164,30 @@
 } // namespace impl
 } // namespace _OMP
 
+static bool isInLastWarp() {
+  uint32_t MainTId = (mapping::getNumberOfProcessorElements() - 1) &
+                     ~(mapping::getWarpSize() - 1);
+  return mapping::getThreadIdInBlock() == MainTId;
+}
+
 bool mapping::isMainThreadInGenericMode(bool IsSPMD) {
   if (IsSPMD || icv::Level)
     return false;
 
   // Check if this is the last warp in the block.
-  uint32_t MainTId = (mapping::getNumberOfProcessorElements() - 1) &
-                     ~(mapping::getWarpSize() - 1);
-  return mapping::getThreadIdInBlock() == MainTId;
+  return isInLastWarp();
 }
 
 bool mapping::isMainThreadInGenericMode() {
   return mapping::isMainThreadInGenericMode(mapping::isSPMDMode());
 }
 
+bool mapping::isInitialThreadInLevel0(bool IsSPMD) {
+  if (IsSPMD)
+    return mapping::getThreadIdInBlock() == 0;
+  return isInLastWarp();
+}
+
 bool mapping::isLeaderInWarp() {
   __kmpc_impl_lanemask_t Active = mapping::activemask();
   __kmpc_impl_lanemask_t LaneMaskLT = mapping::lanemaskLT();
@@ -220,7 +230,7 @@
 static int SHARED(IsSPMDMode);
 
 void mapping::init(bool IsSPMD) {
-  if (!mapping::getThreadIdInBlock())
+  if (mapping::isInitialThreadInLevel0(IsSPMD))
     IsSPMDMode = IsSPMD;
 }
 
diff --git a/openmp/libomptarget/DeviceRTL/src/State.cpp b/openmp/libomptarget/DeviceRTL/src/State.cpp
--- a/openmp/libomptarget/DeviceRTL/src/State.cpp
+++ b/openmp/libomptarget/DeviceRTL/src/State.cpp
@@ -366,7 +366,7 @@
 
 void state::init(bool IsSPMD) {
   SharedMemorySmartStack.init(IsSPMD);
-  if (!mapping::getThreadIdInBlock())
+  if (mapping::isInitialThreadInLevel0(IsSPMD))
     TeamState.init(IsSPMD);
 
   ThreadStates[mapping::getThreadIdInBlock()] = nullptr;