check how == 'S'

Author: aram-cedarwood

pandas/core/arrays/period.py

@@ -811,7 +811,14 @@ def to_timestamp(self, freq=None, how: str = "start") -> DatetimeArray:
 
         new_parr = self.asfreq(freq, how=how)
 
-        new_data = libperiod.periodarr_to_dt64arr(new_parr.asi8, base)
+        is_start = how == "S"
+        if is_start:
+            new_data = np.asarray(
+                [getattr(period, "start_time", period) for period in new_parr]
+            )
+        else:
+            new_data = libperiod.periodarr_to_dt64arr(new_parr.asi8, base)
+
         dta = DatetimeArray._from_sequence(new_data, dtype=np.dtype("M8[ns]"))
 
         if self.freq.name == "B":

pandas/tests/indexes/period/methods/test_to_timestamp.py

@@ -141,6 +141,18 @@ def test_to_timestamp_1703(self):
         result = index.to_timestamp()
         assert result[0] == Timestamp("1/1/2012")
 
+    def test_cast_to_timestamps_at_beginning_of_period(self):
+        # GH 59371
+        index = period_range("2000", periods=3, freq="M")
+        result = index.to_timestamp("M")
+
+        expected = DatetimeIndex(
+            ["2000-01-01", "2000-02-01", "2000-03-01"],
+            dtype="datetime64[ns]",
+            freq="MS",
+        )
+        tm.assert_equal(result, expected)
+
 
 def test_ms_to_timestamp_error_message():
     # https://github.com/pandas-dev/pandas/issues/58974#issuecomment-2164265446