USB-C as power source and negotiation with USB 2.0 and 3.0
When you plug in your device the pull up resistor Rp on the host side and pull down resistor Rd on the device side form a resistor divider.

The Rd resistor is 5.1K as you mentioned, but the Rp will vary based on the power capabilities of the host. You can monitor the voltage at the cc pins, and after making sure the host is capable of providing enough power, enable the power demanding circuitry.
AN5225 by ST talks more about the issue.