The swimming isn’t what you think. It’s also called the diving reflex for good reason: https://en.wikipedia.org/wiki/Infant_swimming#/media/File:Ba...

As a baby I fell into a pool and needed to be rescued. I didn’t inhale water, but as generally happens I very much did just sank to the bottom. Babies can be taught to float at around 5 months, but it’s not reflexive.