For occasions like this, sed -n can come in handy. With sed -n, sed doesn't print anything on output by default, so you can make a command that prints certain lines, like a sort of overpowered grep:
$ printf '12:23:00 foo\n13:45:23 bar\n15:43:12 baz\n' |
sed -ne '/^13:/,$p'
/^13:/,$ means "for the lines starting with the line that starts with 13: and ending with the end of the file", and p means "print".
In other words, print the part of the file that starts with the line that matches the regex. In the example, "foo" came before the "13:" line, so it wasn't printed.