Fighting with an infant in your arms is beyond impractical even if using said infant as a mass1. Any techniques will not work as expected, your balance will always be off (infants do struggle), and you will have to always worry about harm coming to the infant.
So, run towards safety as fast as you can. Shielding your infant should be a priority so using your own body as a shield between them and whatever the threat is.
Obligatory link to no nonsense self defence where you can learn a little more about how to keep yourself out of trouble in the first place. This should be your goal: Not being there when violence starts is the safest thing to do.
Martial arts… Maybe?
Kicks are good but balance will be a problem although you can practice that with weights. However, a struggling screaming infant is a different thing. The last thing you want is to end up on the floor.
Punches will be much less powerful than if you could put your whole body behind them thus are unlikely to do much good.
In this situation, the less said about grappling, the better…
Weapons, such as knives, guns, or CS-gas are all possibles but escalate the situation massively and can be illegal to use. What is you lose control of the weapon? Not a good idea at all.
However, one of the things that will help is your increase in self confidence from doing martial arts. It will make you appear less like prey and more like a predator.
1 Clearly a suboptimal substitute for a mass and said in jest. Do I need to say that⸮…