Yes, the pins are tiny, butt the end pins are double pins on the connector and just about solderable (0.6mm wide for two pins together).
However, whilst this works when you use a legacy cable from a USB-A, giving 5V, this will not work to a true USB-C power supply or device.
Well, resistance is not futile, it seems. There are two connectors (CC1 and CC2) on the USB-C which need resistors to GND to tell the other end you want power.
Whilst the end power connections are two pins at a time (0.6mm), the CC1/2 pins are not, and are 0.3mm wide at 0.5mm spacing. That is pretty much impossible to mill, as the milled track is anything from 0.3mm to 0.6mm wide. The picture above shows around 0.5mm milled track, which is deliberately spaced to allow soldering to the pin 6th from the right. So double pin on right (GND), next double pin in (VBUS) and then another pin we don't care for and then the CC pin. Same on the other side of the connector, except the CC pin is next to the VBUS on that side.
Yes, it is possible to solder!
Then to add the 5.1kΩ resistors to GND.
The end result is power from USB-C...
P.S. Thanks to John for pointing this out to me.
P.P.S. John also pointed out that you do need the two resistors - and cannot simply common up CC1/CC2 with one resistor (as RasPi4 did, by mistake).