Sorry, I am not sure I am understanding what you are wanting to do.
I understand that you are receiving data from an FPGA over SPI, but it is unclear how you want to see on your PC.
That is there are lots of different options for things like:
a) You receive a buffer from SPI, and then you simply do something like: Serial.write(buffer, len); which will write the
binary data over the USB Serial, where you can have something like python or the like on the PC to do something with it.
b) You can potentially write the data you receive to a file system. Could be SD card connected either through SDIO or SPI. Could
be using LittleFS to unused portion of the Flash on your board, or other options. How you get that to your pc depends.
SD Card, you could remove and then read it like any other SD card. You could setup your sketch on the Teensy to support MTP
Which you can then connect up to your PC and download it using MTP.
Or there are probably many other options as well, but hard to guess without knowing more what you are trying to do.