Sometimes we use the -ing form of a verb with "get".
Let's get moving.
Let's get going.
The verbs "going" and "moving" can indicate actions that happen over a period of time. Once you start moving or going, it is possible to continue. However, once you start, you cannot continue to start. You can continue what you started to do, but the "starting" is complete. So we don't say, "Let's get starting."
Sometimes it occurs with the past of "get".
When we finally got to talking about it, it took a long time for the conversation to end.
Once again "talking" is something that can happen over a period of time. Therefore, the -ing form of the verb can work in this way.