The second institution is better.
Tianjin Jinbao Jewelry Supervision and Inspection Center is the only legally established jewelry supervision and inspection institution in Tianjin and a member of the National Jewelry and Jade Standardization Technical Committee. There are specialized institutions in official website to make inquiries.
The Geological Bureau can also do jewelry testing, many of which are composition testing of rocks and jade.
Compared with the second one, of course, as long as your baby belongs to jade in a broad sense, both institutions can detect it.
I hope the answer can help you.