"On Monday we learn."
Translation:Am Montag lernen wir.
It is not about the word order of "Wir", but rather the word order of the verb. In this sentence, "Lernen wir" is used because the verb always comes at the second spot. While "Guten Tag, Wir beginnen!" has 2 phrases "Guten Tag" and "Wir beginnen". For "Wir beginnen", the verb is rightly placed at the second spot.