One set of instructions; two gauges, with two different yarn / needle combinations, give us the two different hat sizes - newborn & infant. You’ll only need one needle size per hat. (Although, if you’d like to add the optional ties, I recommend 2 dpns in a size or two smaller than your hat needle.)

My recommendations:

Use sport weight Terne with either a US #2 / 2.75mm or US #3 / 3.25mm needle for the 0-3 month size.

Use DK weight Lerke with either a US #5 / 3.75mm or US #6 / 4.0mm for the 3-6 month size.