The cause of meningitis is strongly age-dependent. In the first weeks of life the offending bacteria come mainly from the mother's vaginal and gastrointestinal flora, giving the well-known trio of Group B $Streptococcus$, $E.\ coli$ and $Listeria\ monocytogenes$.
A $6$-week-old still falls within this early-infancy pattern. Of the four answer choices, only $Listeria$ belongs to that maternal-flora group, making it the best response. $S.\ pneumoniae$ and $H.\ influenzae$ dominate later in infancy and childhood once passive maternal immunity declines, and $S.\ aureus$ is tied to surgery, trauma, or indwelling devices rather than spontaneous infant meningitis.
This is also why guidelines pair ampicillin with a third-generation cephalosporin in this age group: the cephalosporin alone misses $Listeria$.
\[\boxed{\text{Listeria monocytogenes}}\]