Doing this without I2S, I would imagine an interrupt for each falling edge probably requires more CPU time than Teensy 3.6 can offer. Even overclocked to 240 or 256 MHz, this is probably too much.
But DMA might be able to do it. Maybe. The performance info can be found on page 576. Running at 180 MHz, this would seem to mean you could get 10 million DMA requests per second.
You'd probably configure a DMA channel to trigger on the falling edge from a pin, and in the DMA's TCD you'd have it copy the GPIO's pin read register to a buffer in RAM. Then in your program you'd have to write code to read the bytes or words from that buffer, pull out the 1 bit for the data pin, assemble groups of 33 into the frames, and do whatever analysis you want... while keeping up with the arrival rate of 10 million new bytes per second.
Any of these ways will require you to get into some fairly low-level programming. Maybe some of the code from the audio library can help. We can try to answer questions here, but the reality of helping with this sort of proprietary system where you can't give details, well, it's less than ideal. You're going to have to figure out most of these details from the info in the reference manual.
Hopefully this advice can at least start you on the paths that have some chance of working within the limits of the hardware.