diff --git a/doc/source/whatsnew/v1.3.2.rst b/doc/source/whatsnew/v1.3.2.rst
index bcb096e630d85..70fff75f84dc3 100644
--- a/doc/source/whatsnew/v1.3.2.rst
+++ b/doc/source/whatsnew/v1.3.2.rst
@@ -32,6 +32,7 @@ Bug fixes
 ~~~~~~~~~
 - Bug in :meth:`pandas.read_excel` modifies the dtypes dictionary when reading a file with duplicate columns (:issue:`42462`)
 - 1D slices over extension types turn into N-dimensional slices over ExtensionArrays (:issue:`42430`)
+- Fixed bug in :meth:`Series.rolling` and :meth:`DataFrame.rolling` not calculating window bounds correctly for the first row when ``center=True`` and ``window`` is an offset that covers all the rows (:issue:`42753`)
 - :meth:`.Styler.hide_columns` now hides the index name header row as well as column headers (:issue:`42101`)
 - Bug in de-serializing datetime indexes in PYTHONOPTIMIZED mode (:issue:`42866`)
 -
diff --git a/pandas/_libs/window/indexers.pyx b/pandas/_libs/window/indexers.pyx
index d188770576e05..197345b3ce6ac 100644
--- a/pandas/_libs/window/indexers.pyx
+++ b/pandas/_libs/window/indexers.pyx
@@ -79,12 +79,11 @@ def calculate_variable_window_bounds(
     else:
         end[0] = 0
     if center:
-        for j in range(0, num_values + 1):
-            if (index[j] == index[0] + index_growth_sign * window_size / 2 and
-               right_closed):
+        end_bound = index[0] + index_growth_sign * window_size / 2
+        for j in range(0, num_values):
+            if (index[j] < end_bound) or (index[j] == end_bound and right_closed):
                 end[0] = j + 1
-                break
-            elif index[j] >= index[0] + index_growth_sign * window_size / 2:
+            elif index[j] >= end_bound:
                 end[0] = j
                 break
 
diff --git a/pandas/tests/window/test_rolling.py b/pandas/tests/window/test_rolling.py
index 77ca482936298..5bf2df0208ddc 100644
--- a/pandas/tests/window/test_rolling.py
+++ b/pandas/tests/window/test_rolling.py
@@ -220,6 +220,36 @@ def test_datetimelike_centered_selections(
     tm.assert_frame_equal(result, expected, check_dtype=False)
 
 
+@pytest.mark.parametrize(
+    "window,closed,expected",
+    [
+        ("3s", "right", [3.0, 3.0, 3.0]),
+        ("3s", "both", [3.0, 3.0, 3.0]),
+        ("3s", "left", [3.0, 3.0, 3.0]),
+        ("3s", "neither", [3.0, 3.0, 3.0]),
+        ("2s", "right", [3.0, 2.0, 2.0]),
+        ("2s", "both", [3.0, 3.0, 3.0]),
+        ("2s", "left", [1.0, 3.0, 3.0]),
+        ("2s", "neither", [1.0, 2.0, 2.0]),
+    ],
+)
+def test_datetimelike_centered_offset_covers_all(
+    window, closed, expected, frame_or_series
+):
+    # GH 42753
+
+    index = [
+        Timestamp("20130101 09:00:01"),
+        Timestamp("20130101 09:00:02"),
+        Timestamp("20130101 09:00:02"),
+    ]
+    df = frame_or_series([1, 1, 1], index=index)
+
+    result = df.rolling(window, closed=closed, center=True).sum()
+    expected = frame_or_series(expected, index=index)
+    tm.assert_equal(result, expected)
+
+
 def test_even_number_window_alignment():
     # see discussion in GH 38780
     s = Series(range(3), index=date_range(start="2020-01-01", freq="D", periods=3))