How arduino boards eliminate the need to press buttons to flash?
I'm not familiar with this board, but according to this schematic:
https://wiki.wemos.cc/_media/products:lolin32:sch_lolin32_v1.0.0.pdf

U4 (one of the small 6-leg components) connects to IO0 (pin 25) on the ESP-32. The transistor inside U4 combines the RTS and DTR signals (from U6 USB-Serial converter IC, which will be the large IC marked SIL2104) to put IO0 in the correct state for flashing. The RTS and DTR signals can be set by the host (the computer doing the flashing).

Apologies for the lack of depth, but the short answer is components U4 and U6 on the board work together on the command from the host computer to put IO0 in the correct state for flashing.