I think it’s a tactic similar to ad hominem. They just want to silence opposition to their narrative by throwing out a brutal accusation. They don’t actually care about infants or babies in Ukraine, and if you press them, they aren’t likely to know anything more about this “story” than what they’ve already said. That is one way to expose them. Ask for more details and force them to reveal their ignorance. It’s easy too because you, in this position, have just learned about this atrocity and could naturally be expected to ask a bunch of questions: who was it, where was it, what were their names, when was it, are they okay, what did the authorities see, do you have a link with more details/photos/videos, is there a place to donate, has this been reported to international watchdogs, etc. If the person has no further details, yet has known about this “story”, then it reveals their true apathy.

The other tactic is to ask them why they haven’t gone to the front lines of Russia to fight with Ukraine themselves. Remind them that all men and women fighters are welcome and free to go. Make the warmonger own his warmonging, and make him explain all his excuses for why he must only pound the war drums for others to fight but he must stay home. Pretty much whatever he says at this point is going to sound ridiculous. Because whatever he says he is now putting above the atrocity he just pretended to care so much about. This makes it easy to reframe the guy socially as either a coward or a hypocrite.