Unfortunately, Fragrantica doesn't even "green fig" as a note ...

Try just "fig" (that will get some things that have a dried-fig note, but also things with the fresh/green fig note you're looking for -- hopefully you can get an idea from the descriptions which is which). They also have "fig leaf" and "fig tree" on their drop-down menu.

do businesses online other than BPAL send out little testers?

Generally, mainstream perfume companies won't do so directly, but you can buy little sample vials from decant websites like Surrender To Chance.