Like most audio DACs, internally it uses
delta-sigma modulation, so it can only work if you supply a stream of audio samples at a consistent rate. It doesn't work if you send just one 16 bit sample. If fact, the chip even has a special low power reset mode at startup which is only ended when it hears a steady MCLK signal. The hardware through and through is designed for a steady stream of samples at a consistent audio sample rate.
2 communication channels are used between the SGTL5000 chip and Teensy, I2C for configuration and I2S for the audio stream data. Even though the names look similar, they are nothing alike. Both have special hardware inside the processor which is very powerful but also quite complex. Normally software libraries like Wire and Audio are used to access that hardware, since writing your own code to directly manipulate the hardware is a huge project which would take even the most experienced firmware developers quite a lot of time and effort.
The Teensy Audio Library really is pretty easy to use. This tutorial is the place to start. It's 31 pages covering a lot of features, but just getting the hardware to make test beeps is covered on page 3, and playing music from the SD card is covered on page 4. There is also a full walkthrough video, if you get stuck or if you just prefer to watch and hear a demo rather than read 31 pages.
https://www.pjrc.com/store/audio_tutorial_kit.html
If you *really* want to dive into the difficult low-level details of how to use the hardware to talk to the SGTL5000 chip, you certainly can. But it's a steep learning curve. You can find working code inside the audio library. Of course the hardware is documented in the
reference manual. The I2S hardware is covered in chapter 38 starting on page 1985. But alone that hardware usually isn't very useful. It's almost always used together with DMA, which is covered in chapter 6 starting on page 89.