When abstract logic circuits get translated to the electrical equivilant, how are conversions from 0 to 1 handled?
Why do you think it is absurd for every gate to be connected to power source? That's exactly how it works. Here is a schematic representation of a CMOS inverter:



When the input is low, P-channel device is conducts, thus pulling the output high. When input is high, N-channel device conducts and brings output low.

You can also have variants with passive pull-up or pull-down, but none of them "make" power.