08/28/888, more than 1,100 years earlier
In more detail:
• 02/02/2000 is the first date in February with no odd numbers.
• Move back a month, and it's January: 01.
• Move back another month, and it's 1999.
• Move back a millennium: 1000-1999.
• Move back another decade: 889-999.
• Finally, the year 888 contains no odd numbers!
• Dec., Nov., and Oct. of 888 each contain an odd number: 12, 11, 10.
• September also has an odd number: 09.
• The last three days of August contain odd numbers: 31, 30, 29.
• Finally, August 28, 888 contains no odd numbers: 08/28/888