I suspect you’re right - that the adapter is the issue, but what’s strange is that it came with an extremely fast external SSD. Because of that, I assumed it would support USB 3.0 for data transfer.When you bought the no-name USB-C to -A adapter did it claim to be USB 3 or 3.1. I suspect it didn't and is only USB 2.
The excuse is that these cables are sold for people who want to simply charge USB-C devices. You have to check the specs carefully as a connector alone is not enough. Is the cable a thin cheap looking cable?