Hi Luke,
You indicate what you entered not what it is supposed to mean,
we don't really know what your regional date formatting is.

But you can best check out for yourself what you actually
have upon entry by including another column.   Okay most of
us know that you have 06 for June,  and 02 for the day of the
month, but you should be checking it out for yourself and
then you'd know it's not the year.

A1:   06/02
B2:   =A1    format  as   yyyy-mm-dd hh:mm   though the time will all be 00:00

As long as you not put in a full date excel will assume a full date, so if
you enter 6/2 excel will assume June 2nd current year, you need to enter
06/01/02 and a custom format mm/yy or mm-yy will give you what you want.
Else you would need to precede entry with an apostrophe ' to get a text date