USB C to Thunderbolt
No. 

Thunderbolt is a protocol for combining PCI express data with DisplayPort video protocols. (i.e. super high speed - low latency protocol for display, networking, data and power transfer)

USB is a serial protocol for increased speeds and backwards compatibility with USB 2.0 and 1.1 It doesn't include PCI express or DisplayPort but does have data and power transfer capabilities.

DisplayPort can carry HDMI signals since it is basically a more capable / flexible standard. HDMI cannot accommodate DisplayPort though. Think of a pickup truck and a motorcycle. You can put some motorcycles in some trucks, but generally never the reverse. 

USB Type-C is a physical connector that can be used for USB as well as Thunderbolt 3 protocols which is confusing to say the least to many. The DisplayPort embedded over USB 3.1/Type-C is something that's ready today and makes it less necessary to have thunderbolt for many video applications today on the newest hardware.