Then reduce your flash output, or bounce. Note that some flashes may fire a pre-shot strobe to evaluate metering, and the diffuser may confuse the camera into thinking it needs to boost the flash output. So best to override or bounce.
Overwhelming does not sound like an issue with the infant, rather an issue with flash / camera settings. Or are you concerned about possible side effects on the eyes of the child? However irritating a flash might be, it is not harmful in any way. But of course, scaremongers will never agree
Using flash to take photo of my kids. Bounced or softbox won't make much different. Infant eyes are yet to fully developed and "diffused" in nature. By the time they can focus and see things sharply, they are as good as adult eyes.
Agree best to use natural light. The effect of direct flash for portraits is usually just awful, perhaps even more so on an infant. It's not like the infant is going anywhere, got lots of time to get the lighting right.