Make an external staircase to the basement from concrete?

Hello, I also have questions on this topic. My builder is charging an additional 12,000 euros for an external basement staircase. Which I find too expensive. Now I wanted to do it myself. I wanted to have a ready-made staircase installed (the crane will be on the construction site anyway). My question is: Can I connect the rainwater that accumulates in front of the basement door to the house drainage? Or should I better cover it. But that will be more expensive. Regards Frico26