There are several different projects to provide access to the underneath solder pads.
For pads 24-33, the 2x5 SMD headers can be used like MJS513 says.
FRDM4236/Trainer4edu has two different PCB designs that can order from OSH park that brings out the pins in a form factor similar to the Teensy 3.6, including attaching pads 34-39 to a micro SD card reader. One pad brings out the USB host pins, and the other pad only brings out pads 24-39:
In the FRDM board, you will need to order a few surface mount components (capacitors, resistors, micro SD card reader). The board uses castellated cut-outs for the pins, so you need to make sure the PCB fab does the cut out correctly. As the FRDM site mentions, he had some problems with the thinner PBCs getting everything to match up.
Blackketter has a board that brings out the pins in a smaller fashion than the FRDM board, adding a row of 14 pins on each side of the Teensy. Blackketter also has side car PCBs to allow easier addition of the micro SD card reader, USB host, and integration with a ESP32 wifi/bluetooth board.
In soldering the 1mm pads for pads 34-39, IMHO, the FRDM board is slightly easier to solder than the blackketter board.
Talldog (on tindie) and loglow (here) has a board he has been designing that he was planning to sell on his tindie site.
Many of us wish that Paul could get the appropriate parts to announce and sell a Teensy 4.x variant (4.1?) that will have more pins and be in the Teensy 3.6 form factor. But until that happens, you have the various DIY approaches.
The original breakout board was used during the Teensy 4.0 beta test period. It uses pogo pins to access some of the pads in the 24-33 range (but not all pads were brought out), and it uses a FFC cable to bring out the SD pads. One of the main features is providing for a separate pad to allow using a revision A/B/C audio shield with the Teensy 4.0. With the revision D shield now shipping, we don't really need that section of the board.