diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 325c94d0ea267..c3fbd716ad09d 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -2202,7 +2202,9 @@ def validate_periods(periods: int | float | None) -> int | None:
     return periods  # type: ignore[return-value]
 
 
-def validate_inferred_freq(freq, inferred_freq, freq_infer):
+def validate_inferred_freq(
+    freq, inferred_freq, freq_infer
+) -> tuple[BaseOffset | None, bool]:
     """
     If the user passes a freq and another freq is inferred from passed data,
     require that they match.
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index d9f6cecc8d61d..7a56bba0e58b3 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -264,7 +264,10 @@ def _validate_dtype(cls, values, dtype):
     # error: Signature of "_simple_new" incompatible with supertype "NDArrayBacked"
     @classmethod
     def _simple_new(  # type: ignore[override]
-        cls, values: np.ndarray, freq: BaseOffset | None = None, dtype=DT64NS_DTYPE
+        cls,
+        values: np.ndarray,
+        freq: BaseOffset | None = None,
+        dtype=DT64NS_DTYPE,
     ) -> DatetimeArray:
         assert isinstance(values, np.ndarray)
         assert dtype.kind == "M"
@@ -291,7 +294,7 @@ def _from_sequence_not_strict(
         dtype=None,
         copy: bool = False,
         tz=None,
-        freq=lib.no_default,
+        freq: str | BaseOffset | lib.NoDefault | None = lib.no_default,
         dayfirst: bool = False,
         yearfirst: bool = False,
         ambiguous="raise",
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index fe101926a6782..427c744b92a0a 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -1746,7 +1746,7 @@ def to_numpy(
         self,
         dtype: npt.DTypeLike | None = None,
         copy: bool = False,
-        na_value=lib.no_default,
+        na_value: object = lib.no_default,
     ) -> np.ndarray:
         """
         Convert the DataFrame to a NumPy array.
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index f776585926024..3a7adb19f1c01 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -25,6 +25,7 @@
     lib,
 )
 from pandas._libs.tslibs import (
+    BaseOffset,
     Resolution,
     periods_per_day,
     timezones,
@@ -312,7 +313,7 @@ def isocalendar(self) -> DataFrame:
     def __new__(
         cls,
         data=None,
-        freq=lib.no_default,
+        freq: str | BaseOffset | lib.NoDefault = lib.no_default,
         tz=None,
         normalize: bool = False,
         closed=None,
diff --git a/pandas/core/internals/array_manager.py b/pandas/core/internals/array_manager.py
index 3a8ed54d6c634..88f81064b826f 100644
--- a/pandas/core/internals/array_manager.py
+++ b/pandas/core/internals/array_manager.py
@@ -1132,7 +1132,7 @@ def as_array(
         self,
         dtype=None,
         copy: bool = False,
-        na_value=lib.no_default,
+        na_value: object = lib.no_default,
     ) -> np.ndarray:
         """
         Convert the blockmanager data into an numpy array.