The incident, which remains under investigation by British Transport Police, saw 15-week-old Esme Emmerson hit by flying glass.
She was travelling with her parents Jason Emmerson and Kristina Vojsovicova on the 3pm Northern service from Bridlington to Hull when the incident happened close to Snuff Mill Lane at 3.45pm.
Tony Baxter, regional director for Northern, said: “In our experience, this sort of attack is rarely the action of a ‘lone wolf’ and more likely the reckless pastime of a group that think it’s fun to throw things at fast moving trains.
“The perpetrator has had a month to turn themselves in and has chosen not to – so it’s time for someone who was with them and knows what happened to come forward and help British Transport Police with their investigation.”
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“The consequences of a brick hitting a fast-moving train are potentially devastating and we can only give thanks that little Esme wasn’t more seriously injured.”
Anyone with information can contact BTP by texting 61016 or by calling 0800 405040. Alternatively, people can call Crimestoppers, anonymously, on 0800 555111.