Accessing Time Capsule Cable vs Wireless

Can I use an ethernet cable to make this happen more quickly?

Yes, this would be highly recommended since the data transfer will likely be 2-5 times faster than WiFi as well as more reliable.

If so what type of cable is recommended to covert from the ethernet port on the TC, to the Thunderbolt 3 (USB-C) ports on the laptop?

Use a USB-C to Ethernet adapter with a standard Ethernet cable. Apple recommends and sells the Belkin adapter for this purpose. See details below:

https://www.apple.com/shop/product/HJKF2ZM/A/belkin-usb-c-to-gigabit-ethernet-adapter

The adapter is also available from most big box electronic stores like Best Buy and online from Amazon.

https://www.amazon.com/Belkin-USB-C-Gigabit-Ethernet-Adapter/dp/B01GLN3LZA/ref=sr_1_4?crid=345E02OLTC97Q&dchild=1&keywords=belkin+usb-c+to+gigabit+ethernet+adapter&qid=1614868202&sprefix=belkin+usb-c+to%2Caps%2C184&sr=8-4

Edit to post above.

If you decide to use the USB-C to Ethernet adapter, be sure to turn off the WiFi on the Mac to insure that the connection will be over wired and not wireless, since most newer Macs will default to WiFi even if another connection is present.