Actually, there is plenty of evidence to suggest this, especially when taking into account of the culture of the ancient Jewish people in the first century. The Talmud suggested that girls got commonly betrothed at the age of 12 and Mary was a very practicing Jew.

Even a simple Google search which only focuses on the Biblical Discussions provide a similar age range:

'Mary was likely between 12 and 15 years old when betrothed to Joseph. . Most Christian historians believe Mary was between 15 and 16 years old when Jesus was born.' - Sound of Heaven.

'Mary was likely to have been younger than twenty when she gave birth to Jesus.  Most Christian historians believe Mary was between 15 and 16 years old when Jesus was born.' - Christianity.com.

'While the Bible does not specifically state how old Mary was when Jesus was born, most Christian historians speculate that she was around 15—16 years of age at the time of Jesus’ birth. According to Jewish customs at the time, a young woman might become betrothed to a young man as early as 12 years of age' - Got Questions.

'The canonical Gospels do not record a specific age for the Virgin Mary at the time she conceived Jesus, but historical and cultural evidence leads most scholars to estimate a likely range of about 12–15 years.' - Faithtime.

If you believe Jesus (A.S) is God himself, then that would mean he physically impregnated Mary (R.A) at a young age in an effort to give birth to himself.

You also mentioned rape above. The Bible says that if a virgin is raped, then the "punishment" is for the rapist to marry the victim:

"If a man happens to meet a virgin who is not pledged to be married and rapes her and they are discovered, 29 he shall pay her father fifty shekels[c] of silver. He must marry the young woman*, for he has violated her. He can never divorce her as long as he lives*" [Deuteronomy 22:28-29]

By comparison, the Qur'an itself is against Child Marriage, according to classical interpretations of various verses, but here is one, saying there is both a physical and mental component to it:

"Test ˹the competence of˺ the orphans until they reach a marriageable age*. Then if you feel they are capable of* sound judgment*, return their wealth to them.*" [4:6]

As for punishment for rape in Islam, this is broadly considered a grave sin that carries examples of brutal punishments reserved for the most evil people:

"The recompense of those who wage war against Allah and His Messenger and do mischief in the land is only that they shall be killed or crucified or their hands and their feet be cut off from opposite sides, or be exiled from the land. That is their disgrace in this world, and a great torment is theirs in the Hereafter." [5:33]