Warning
Note that the only legal way of obtaining a BIOS image is to dump it from your own Playstation 2 console.
Do not attempt to ask where to get BIOS images on the PCSX2 forums, because it's against the forum rules.
The PS2 BIOS is a copyrighted material of Sony Corporation.
It is illegal to distribute the copyrighted files without copyright holder consent. PCSX2 team
could get in trouble if suspected of illegally supplying people with BIOS files!

If your BIOS image does not appear in the BIOS images list and you are sure that you have selected the correct folder,
you may what to try dumping your BIOS again because the one you have is probably not valid or corrupted.
Note that it is not recommended to use the first Japan version of BIOS (SCPH-10000.bin).
You will probably be able to run the games with it but there is a chance to affect compatibility somehow.
Although the first PS2 consoles should be really hard to get these days.

Lightbulb.png Tip:
Interesting fact: For maximum compatibility it is recommended that you use a BIOS image different than SCPH10000.BIN which is the oldest one.
That's because with this BIOS there are problems in memory card emulation and in other sections. auMatt.
https://wiki.pcsx2.net/Setting_up_Windows_version#BIOS

SCPH-10000.binはダメです