Well unless you are wedded to using a Teensy 3.2, another option is to get the Teensy 4.1 (which has a built-in SD card slot) and the new SmartMatrix display made for the Teensy 4.0/4.1 (note, the display made for the 3.5/3.6 won't work on the Teensy 4.0/4.1 as the pins are different). I have a Teensy 4.1 that displays animated 64x64 gifs on my current Adafruit display (and I've used 64x32 displays before that). The gifs are stored in the SD card on the Teensy 4.1.
In theory, you could get the current shield for the Teensy 3.x boards and upgrade to the Teensy 3.5/3.6 which have a SD card reader, but the last I checked, the Teensy 3.5/3.6 were sold out everywhere due to chip shortages (when it was available, the Teensy 3.5 was slightly cheaper than the 4.1 but the Teensy 3.6 was slightly more expensive).
Another alternate would be to use the device you have an add a separate USB card reader. Note, the APA102 support can't be used, since that uses pin #13 which is the SPI SCLK pin (and the SmartMatrix device uses pin #14, which is the alternate SCLK pin). However, if you are carrying the Teensy/display, you probably don't want a SD card reader flopping about.
If you don't want to do soldering, you can order a 4.1 with pins already soldered in and it fits in the SmartMatrix board. If you want to attach the 4.1 to the display directly, on many of the displays you might need to cut off the pins beyond pins 12 and 13, as those pins might interfere with the placement of the board (or use the 2x8 cable). As they say in the guide, there is one breakaway tab on the Teensy 4.0 SmartMatrix shield that needs to be removed to use the 4.1, due to the longer board length.
I tried using the APA102 cable for powering the Teensy, and I eventually gave up due to power issues. I just cut the cable from the board.
Good luck.
