According to Advaita Vedanta, we i.e. Jivas are all Brahman in reality but are under Maya and Avidya. I want to know how Maya and Avidya came into Brahman?
P.S. I am aware that Maya has no beginning.
Simply because you have created Maya and avidya for yourself and dropped down to the plane of dual perception. It is due to this duality that such a question has arisen. Remove it and experience non duality—the supreme reality, the highest sense of perception.
I can tell about the Philosophy but don't ask me about any Sanskrit source.
In the Tantra traditions, Goddess Shakti is Mahamaya. She is the feminine essence of the Purusha/Prakriti duality and she is the one creating the illusions. These illusions are what creates something we call incentive structure in Economics. So, in Samsara, (which by the way means "Migration" because Time is also a manifest of Shakti) nothing is fixed. The different seasons forces people to grow different crops to survive,making people react to Nature to achieve "Artha". Circumstances are created such that there is no permanent peace or war and in times of crisis, the line between Dharma and Adharma blurs which calls for the learned men to theorize Dharma in the given context.
Put another way, if every one realized the ultimate truth of Brahman without having to do anything, the worth would not be appreciated and further even if it is realized without the effort, everybody could do it at birth and would be left with nothing to do in life henceforth. Society would become mechanical just like Marxist Communism akin to "sthiti" but the divine mother is "Shakti-sthiti vinashini" exactly because she does not let this happen.
Men who attain enlightenment eventually leave the Earth and a new crop of foolish individuals are born in their place. Maya thus gives a meaning to life as every individual must traverse his way to attain Enlightenment and know the Brahman, while those who achieve it now try to help others in achieving it.
There is another catch, that of communication. People especially those performing "Tapas" by definition cannot disturb the system by warning others of their action without bearing a cost. If he tells them, then he can't verify the trajectory of events that he had envisioned before warning and if he does not, he would have to bear the burden of not saving them when he could have. This is why a hermitage deep inside the forest surrounded by jivas one does not know or have any concern for is considered good for Tapasya and attaining Enlightenment.
Thus, to conclude, the maya is an essential part of the "Brahmanda" and Goddess Mahamaya a tangible manifestation of the Supreme Brahman. Hope this helps...