Love Bryce’s response! Ideally you want to hit that muscle group again when it is no longer sore and has recovered.
For example if you did Monday Upper A, Tuesday Lower A. Wednesday rest. If your upper is still sore from Monday, take Thursday for another rest day and do Upper B Friday. No harm no foul and it will not hinder any progress.
As you already stated, as your body gets accustomed to the volume of the new program you will be a little less sore as you progress through the weeks.
Lastly, don’t forget to make sure you are doing the things that put your body in to a good point of recovery. Getting your 7-8 hours of sleep in, adequate quantity AND quality of nutrition, and also keeping normal life stressors to a minimum to the best of your abilities.
I did the Your Better Half 1.0 program twice, and am now doing the 2.0 version, I love the frequency/volume and have seen very solid progress throughout. Good luck and happy lifting!