You can try map instead of grep, and just keep the matches. From

    (my $date) = grep m%\w+, \w+ \d\d, \d\d\d\d%, @file;
    $date =~ m%\w+, (\w+ \d\d, \d\d\d\d)%;
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to

    my($date) = map m%\w+, (\w+ \d\d, \d\d\d\d)%, @file;
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If the regex doesn't match, it returns an empty list, so it'll disappear from the results.

Also, if the files are largish and the date always appears near the top, I'd avoid reading in the whole file and just read in, say, the first k of text, as a single string. Then you don't even need map.

    local $/ = \1024;
    my $begin = <F>;
    my ($date) = $begin =~ m%\w+, (\w+ \d\d, \d\d\d\d)%;
    my $time = str2time($date);
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update Thanks to Animator for the hint... You do appear to need the entire file. I don't know what is eeasier, checking the file line by line, as you do, or reading in the whole file as a single string, and processing it that way.

You can achieve that by undeffing $/ instead:

    undef $/;
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I think, for this specific file format, your way is easier.