First to directly answer your question, you would normally just press the pushbutton to connect the Program signal to GND. Hopefully it is easy to see from the schematic that the pushbutton is connected to Program and GND.
But perhaps this does not work because your hardware changes by desoldering and soldering different chips have unintentionally damaged your Teensy 4.1 board?
Before looking for damage to parts, check whether your Teensy 4.1 is the older version which had a MKL02 bootloader chip. During the semiconductor shortages in 2022, Teensy 4.1 boards started to be manufactured with a different bootloader chip. This is documented on the Teensy 4.1 page near the schematic. The new chip has 20 pins rather than only 16, so if you were using a microscope or magnifier while soldering, you probably should have noticed the pins would not line up properly. Even after soldering, if you use a magnifier or camera with good macro zoom, you should be able to see whether the MKL02 pins line up properly with the pads on the PCB. If you have the newer Teensy 4.1 board designed for a completely different bootloader chip, then desoldering it and attempting to solder a MKL02 which does not even fit properly onto the pads obviously can not work.