I have a hard time understanding how in the 1st century, the apostles Paul and Peter were tortured and murdered by the Romans, but by 380 CE, Christianity was generally adopted by the Roman Empire. This seems like such a short amount of time for such a huge transformation.
What are some factors that led to the speedy Christianization of Europe after the death of the apostles?
I must question your grasp of time. 300 years is a freaken long time. Christianity would only need to increase its share of the population by 0.3% a year to still reach a 90% majority by the end of the 4th century.
The details of Christianity's spread is afaik still contentious because there is not much hard data about how many people where Christian at any specific time up till the point where we can reliably say virtually everyone was (which I'm not sure happened until medieval times).
The most recent things I've read by the historian Peter Heather had him arguing that Christianity in the Roman Empire would've grown till perhaps 10-20% (if anyone wants to check my memory, I'm referencing this lecture specifically) and then stabilised as a minority religion. He contributes Emperor Constantine's state support of Christianity as the primary factor in turning Christianity from a minority into a majority religion.
For more answers, you will find this exact question has been asked before in this thread.