Let’s start with the immaculate conception. In that time in history daughters that could not be married off were exiled. Mary was young, she was not married. She was pregnant. I would have lied too.
Next lets look at Christ’s ressurection…before medical technology many people were unknowingly buried alive. Say for instance if they had lost alot of blood. This would result in a very weak pulse possible not felt by one examining the person. How much blood do you think Christ lost while hanging on the cross? Enough to be ‘passed out’ for 3 days. Absolutely. Possible that when he woke up or came to and realized he was in a tomb covered in a burial shroud after being crucified he ran? Absolutely