BUG: _guess_datetime_format_for_array doesn't guess if first element is '' or 'NaT'

pandas/_libs/tslib.pyi

@@ -16,6 +16,7 @@ def array_with_unit_to_datetime(
     unit: str,
     errors: str = ...,
 ) -> tuple[np.ndarray, tzinfo | None]: ...
+def first_non_null(values: np.ndarray) -> int: ...
 def array_to_datetime(
     values: npt.NDArray[np.object_],
     errors: str = ...,

pandas/_libs/tslib.pyx

@@ -421,6 +421,23 @@ def array_with_unit_to_datetime(
 
     return oresult, tz
 
+@cython.wraparound(False)
+@cython.boundscheck(False)
+def first_non_null(values: ndarray) -> int:
+    """Find position of first non-null value, return -1 if there isn't one."""
+    cdef:
+        Py_ssize_t n = len(values)
+        Py_ssize_t i
+        int result
+    for i in range(n):
+        val = values[i]
+        if checknull_with_nat_and_na(val):
+            continue
+        if isinstance(val, str) and (len(val) == 0 or val in nat_strings):
+            continue
+        return i
+    else:
+        return -1
 
 @cython.wraparound(False)
 @cython.boundscheck(False)

pandas/core/tools/datetimes.py

@@ -126,9 +126,8 @@ class FulldatetimeDict(YearMonthDayDict, total=False):
 
 def _guess_datetime_format_for_array(arr, dayfirst: bool | None = False) -> str | None:
     # Try to guess the format based on the first non-NaN element, return None if can't
-    non_nan_elements = notna(arr).nonzero()[0]
-    if len(non_nan_elements):
-        if type(first_non_nan_element := arr[non_nan_elements[0]]) is str:
+    if (first_non_null := tslib.first_non_null(arr)) != -1:
+        if type(first_non_nan_element := arr[first_non_null]) is str:
             # GH#32264 np.str_ object
             return guess_datetime_format(first_non_nan_element, dayfirst=dayfirst)
     return None

pandas/tests/tools/test_to_datetime.py

@@ -2093,21 +2093,23 @@ def test_to_datetime_dta_tz(self, klass):
 
 
 class TestGuessDatetimeFormat:
-    @td.skip_if_not_us_locale
     @pytest.mark.parametrize(
-        "test_array",
+        "test_list",
         [
             [
                 "2011-12-30 00:00:00.000000",
                 "2011-12-30 00:00:00.000000",
                 "2011-12-30 00:00:00.000000",
             ],
             [np.nan, np.nan, "2011-12-30 00:00:00.000000"],
+            ["", "2011-12-30 00:00:00.000000"],
+            ["NaT", "2011-12-30 00:00:00.000000"],
             ["2011-12-30 00:00:00.000000", "random_string"],
         ],
     )
-    def test_guess_datetime_format_for_array(self, test_array):
+    def test_guess_datetime_format_for_array(self, test_list):
         expected_format = "%Y-%m-%d %H:%M:%S.%f"
+        test_array = np.array(test_list, dtype=object)
         assert tools._guess_datetime_format_for_array(test_array) == expected_format
 
     @td.skip_if_not_us_locale