Successfully connecting a USB-C drive in the manner you describe depends on two things, that the drive supports Thunderbolt and can get enough power through the cable and adapter.
I have the Apple Thunderbolt 2 to Thunderbolt 3 adapter and it supports only Thunderbolt devices. It will physically connect to any USB-C device (obviously), it may even pass through enough power to get it to light up some indicator lights, but what it doesn't do is convert the Thunderbolt protocol to USB.
What I did in a similar situation was get a Thunderbolt 3 hub. With the Apple TB2/TB3 adapter I was able to successfully use different USB and Thunderbolt devices with an older Mac Mini that had TB2 ports. On a different Mac, a MacBook Pro, connecting the hub by the TB2/TB3 adapter would trigger a kernel panic. I never did figure out why that happened, but I feel I should mention this since I had a 50/50 success rate. I suspect a software issue given the situation, but I didn't feel the need to investigate the problem as I could easily connect any USB-C drive to the MacBook Pro using an appropriate cable or hub.
Using any USB 3.x USB-C to USB-A cable would allow for connecting to an external USB-C drive that had a female USB-C port. Because of how the USB specification works, there are some USB-C drives that come with a "captive cable" with a male USB-C connector on the end, but given how the question is posed this does not appear to be the case. Some of these drives come with an adapter that has a female USB-C on one side and a male USB-A on the other. These are dangerous adapters that violate the USB specification, so I recommend not using them. Or, if you've already made a purchase that comes with this adapter then only use it with the device that it came with since it could cause a short circuit on the power pins, and potentially cause a fire, if used with some other device.
What allowed USB devices to work with that Mac Mini I had and a Thunderbolt 3 hub was that any hub that complies with the Thunderbolt 3 spec must have a USB controller in it for backward compatibility with Thunderbolt 1 and 2 hosts. It is unlikely to find a Thunderbolt 2 dock that will provide USB-C ports for peripherals. It would be trivial to connect USB-C devices to USB-A ports on a Thunderbolt 2 dock if you did find one, but given that this is likely some old stock that's been sitting on a shelf unsold for many years it might not help in getting the higher speeds because it is using an older USB controller or something.
So, if the USB-C drive supports Thunderbolt, and can run on the power that the TB2/TB3 adapter can pass through then the solution is a simple adapter and cable. If not then it is a device that speaks the USB protocol and you'll need a USB controller in the chain somewhere. There's probably a dozen different ways to put a USB controller in this chain, but some kind of Thunderbolt 3 dock or hub is what I would consider the simplest solution. This won't be an exactly inexpensive solution, but any kind of dock or hub will allow for connecting many USB devices with the higher speed, and provide power to those devices beyond what the Thunderbolt or USB ports on the Mac could provide, and that extra capability could justify the extra cost.