I tried searching for a case similar to mine, but looks like it doesn't exist

We are a family of 3, and have permanent residence in New Zealand. I got an offer for a job in Germany, and applied for blue card at Wellington embassy in NZ 6 weeks back. We are Indian passport holders.
As the visa officer at the embassy said, I received my visa the next week, but my wife and child's visa is still pending. Based on what I read in the forums, the marriage certificate can probably be investigated in India. However, our current residence is in New Zealand, and I am wondering how the process will proceed in our case. Our residence address in India is currently unoccupied.
I arrived in Germany 2 weeks back and have not received any request for any documents. No communication so far.
Is it advisable to enquire the general status at a local office here in Germany? I read that it could further delay the process?
Any advise would be great. To be clear, I am fine with waiting for the bureaucracy to go through their steps, just wondering how the process would work in my case and if we should have any arrangements in India in case there is a background check expected.
Many thanks.