Well since \n is a space character - see below. However it appears to me that anchoring this regex to the beginning of the line is just fine. 
use strict;
use warnings;

while (<DATA>)
{
   if (/\d{2}-\d{2}-\d{4}\s+/)
   { 
       print;
   } 
}   

=Prints:
03-15-2021 21.1.0-s102 2021/03/15:04:00:09 21.1 21.10-s102
21.1.0-s102 2021/03/15:04:00:09 21.1 21.10-s102 03-15-2021  **works**
=cut

__DATA__

03-15-2021-1 21.1.0-s103 2021/03/15:14:16:39 21.1 21.10-s103
03-15-2021-2 21.1.0-s103 2021/03/15:14:16:39 21.1 21.10-s103
03-15-2021 21.1.0-s102 2021/03/15:04:00:09 21.1 21.10-s102
21.1.0-s102 2021/03/15:04:00:09 21.1 21.10-s102 03-15-2021
21.1.0-s102 2021/03/15:04:00:09 21.1 21.10-s102 03-15-2021-4

[download]
I guess that /\d{2}-\d{2}-\d{4}[^-]/would also work?

In reply to Re^2: grep only lines having matched pattern by Marshall
in thread grep only lines having matched pattern by noviceuser

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