According to the new "Annotated Edition" of the Siddur Tehillas Hashem, a Bar Mitzvah bachur should get his first aliya either on Shabbos Mincha time, Monday, Thursday, or Rosh Chodesh.
I assume that the source is from Sefer Haminhagim where it says either Monday, Thursday or Shabbos Mincha time. It does not mention Rosh Chodesh.
What is the source of note in the Tehillas Hashem siddur that one could get his first aliya on Rosh Chodesh?