In Jewish tradition Jews pray in connection to Rosh Chodesh ja'aleh wejavo.
Besides that they 'bless the moon' during the first part of the month.
The moon is the foundation of the jewish calender and fixing the festivals.
I suppose, also the noahide calender is like the Jewish calender, based on moon and sun.
How can a noahide remember the new month ?
Is a noahide also permitted to 'bless the moon', like the jews.?
It is interesting to realise that the new month and to count in months is not so much mentioned in Torah and Tenach.
The first commandment of Israel in Ex.12:2 starts with counting the months in connection with Pesach.
We know from David and Jonathan and Shaul that David did'nt attended the feastmeal of Shaul, which suggested to be kept every new month.
What is very interesting is that the counting of ages is usually in days or years, not mentioning months. In Bereshiet it is rare to read about months.
But...in the story of the mabul of Noach, it suddenly counts the time of the mabul in months and when it started and ended.
It gave me the reason the suggest that also noahides are connected with Rosh Chodesh and maybe also with blessing the moon, like we jews do.
Maybe you can work out this concept also for noahides ??