The course will begin from the 1st Jan.
Der Kurs beginnt am 1. Januar.
Der Kurs beginnt ab dem ersten Januar.
Can we interchangeably use am and ab to show the beginning of something on certain month and date?
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If you are talking about a moment, use »an dem« = »am« (in Englisch: at the).
If you are talking about a period of time, that begins at a certain moment, use »ab dem« (in Englisch: from the).
The beginning of a period of time is not a period of time by itself. It is a moment. So, when you use the verb »beginnen«, you talk about a moment and so you have to use »am«. This means: your first sentence is correct, the second is wrong.
If you want to talk about a period of time, you have to use another verb like »stattfinden« (to take place) for example, in Austria it is then said:
Der Kurs findet ab dem ersten Jänner statt.