Possible, maybe. End up with a working machine? Probably not. There are alternatives like coreboot [1] libreboot [2] system76 [3] but this isn't something that can be flashed to just any board. These alternatives would have to become supported by the manufacturer upstream from the dodgy resellers that end up on Amazon and I don't know if that might actually make it easier for dodgy players to replace it with a backdoor version. The low-end devices like mini-PC's do not have dual firmware options like some of the Asus mobo's and a few other mainstream vendors.
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Is it possible to “install” (“flash”?) an open source BIOS onto a newly bought device?
Possible, maybe. End up with a working machine? Probably not. There are alternatives like coreboot [1] libreboot [2] system76 [3] but this isn't something that can be flashed to just any board. These alternatives would have to become supported by the manufacturer upstream from the dodgy resellers that end up on Amazon and I don't know if that might actually make it easier for dodgy players to replace it with a backdoor version. The low-end devices like mini-PC's do not have dual firmware options like some of the Asus mobo's and a few other mainstream vendors.
[1] - https://coreboot.org/
[2] - https://libreboot.org/
[3] - https://github.com/system76/firmware-open