The news, and the birth
The angels told Maryam: Allah gives you good tidings of a word from Him, whose name will be the Messiah, 'Isa, the son of Maryam — distinguished in this world and the Hereafter and among those brought near (3:45).
She asked how, having never been touched by a man. The answer: Thus Allah creates what He wills. When He decrees a matter, He only says to it, Be, and it is (3:47). And Surah Al 'Imran adds a comparison that settles the whole question: Indeed, the example of 'Isa with Allah is like that of Adam. He created him from dust, then said to him, Be, and he was (3:59). Adam had neither parent, and nobody claims Adam was anything other than a human being.
Surah Maryam gives the birth itself with unusual tenderness — the palm tree, being told to shake it towards her so fresh dates would fall, and being told to eat and drink and be comforted (19:23-26).
The baby who spoke
She brought him back to her people, carrying him, and they accused her. She had been told not to speak, and to point to the child instead. They said: How can we speak to one who is in the cradle a child? (19:29).
And then he spoke. His first recorded words, as a newborn, are the clearest thing in his story: Indeed, I am the servant of Allah. He has given me the Scripture and made me a prophet. And He has made me blessed wherever I am and has enjoined upon me prayer and zakah as long as I remain alive, and dutiful to my mother, and He has not made me a wretched tyrant. And peace is on me the day I was born and the day I will die and the day I am raised alive (19:30-33).
Read that to a child slowly. He describes himself as a servant, mentions his mother, and gives himself the same threefold peace the Quran gave Yahya a few verses earlier. Everything that would later be disputed about him, he answered in his first sentence.
The signs, and the ending
He was given remarkable signs — forming the likeness of a bird from clay and breathing into it so it became a bird, healing the blind and the leper, giving life to the dead. The Quran lists them in 3:49 and 5:110, and after each one it repeats the same four words: by permission of Allah.
That phrase is doing deliberate work, and it is worth saying out loud each time you tell the list, exactly as the Quran does.
On the ending, the Quran is direct: And they did not kill him, nor did they crucify him, but it was made to appear so to them — and Rather, Allah raised him to Himself (4:157-158).
And in Surah al-Ma'idah there is a conversation set on the Day of Judgement. 'Isa is asked whether he told people to take him and his mother as gods besides Allah. His answer: Exalted are You! It was not for me to say that to which I have no right... I said not to them except what You commanded me — to worship Allah, my Lord and your Lord (5:116-117).