BUG: pd.to_datetime with format doesn't work with pd.NA

pandas/core/tools/datetimes.py

@@ -56,7 +56,10 @@
     ABCDataFrame,
     ABCSeries,
 )
-from pandas.core.dtypes.missing import notna
+from pandas.core.dtypes.missing import (
+    isna,
+    notna,
+)
 
 from pandas.arrays import (
     DatetimeArray,
@@ -390,11 +393,17 @@ def _convert_listlike_datetimes(
             format = None
 
     if format is not None:
-        res = _to_datetime_with_format(
-            arg, orig_arg, name, tz, format, exact, errors, infer_datetime_format
-        )
-        if res is not None:
-            return res
+        try:
+            res = _to_datetime_with_format(
+                arg, orig_arg, name, tz, format, exact, errors, infer_datetime_format
+            )
+            if res is not None:
+                return res
+        except ValueError:
+            # GH#42957: ValueError: time data '<NA>'
+            # does not match format '%Y%m%d%H%M%S'
+            if isna(arg):
+                format = None
 
     assert format is None or infer_datetime_format
     utc = tz == "utc"