It’s been a long time since I’ve used the Google Maps app on my iPhone, but I *think* you can. Hopefully, someone who currently uses that app will reply soon.
I’m not sure what you mean by “via GPS”, but you can share directions from Google Maps on iOS, yes. When you are looking at the directions, there is a three dot control to the right of “from”. There is a share option there.
If you mean after you have already tapped Start for navigation, not that I know of, but you can always exit and then share from the directions screen, which is where you should be when you exit navigation.