Likely the string isn't directly castable to datetime or date (like the others I'm guessing because we can't see the data).
Think it'll be based on your OS localisation.
The convert function allows you to tell it what format the date is in to help it out, like this: convert(datatype, data, format)
If your OS localisation dates are UK format (DD/MM/YYYY), try 103:
SELECT
CONVERT(DATETIME, LTRIM(SUBSTRING (Col1, 1, 20)), 103) AS 'DateTimeStamp',
if US format (MM/DD/YYYY), try 101:
SELECT
CONVERT(DATETIME, LTRIM(SUBSTRING (Col1, 1, 20)), 101) AS 'DateTimeStamp',
If neither of these formats, there's a full list at https://msdn.microsoft.com/query/dev10.query?appId=Dev10IDEF1&l=EN-US&k=k(CAST_TSQL);k(SQL11.SWB.TSQLRESULTS.F1);k(SQL11.SWB.TSQLQUERY.F1);k(MISCELLANEOUSFILESPROJECT);k(DevLang-TSQL)&rd=true