What happens when an internet connection is faster than the storage write speed?
Many protocols, including TCP which is most widely used protocol on the Internet, use something called flow control. Flow control simply means that TCP will ensure that a sender is not overwhelming a receiver by sending packets faster than it can empty its buffer. The idea is that a node receiving data will send some kind of feedback to the node sending the data to let it know about its current condition. So, two way feedback allows both machine to optimally use their resources and prevent any problems due to mismatch in their hardware.

https://en.wikipedia.org/wiki/Flow_control_(data)