Hi Cinimo and welcome to Flyertalk! The agent was evidently incorrect, no babies on any airline would be allowed on the exit row. LATAM's own website states one needs to be over 15 to sit on an exit row.

My experience with booking exit rows on LATAM as BA Gold is that it never works online, but the agents on the phone tend to be very helpful. LATAM's site states that Platinum (which is equivalent to Silver) have access to exit rows on domestic travel. (https://www.latam.com/en_un/latam-pass/favorite-seat/). I'd call again.