Proprietary WiFi drivers for live mode

[Kristijonas Lukas Bukauskas <kb@tsig.nl>]

Hello,

I have an old Dell laptop with Broadcom BCM43142 WiFi device
(https://wiki.debian.org/wl). It doesn't have a hard drive, so I
sometimes boot Debian from USB Memory Stick in live mode.
The problem is that WiFi doesn't work because of the proprietary drivers
it needs.

I tried booting it from live+nonfree image
(https://cdimage.debian.org/cdimage/unofficial/non-free/cd-including-firmware/11.3.0-live+nonfree/amd64/iso-hybrid/),
but still no luck (WiFi doesn't work). As I understand, the needed
drivers would load when installing the system, but they do not load in
live mode.

How do I get Wifi working right in live mode? I would prefer Debian, but
any Linux ready-to-use image would work for me.

Thanks for any help!

-- 
Kristijonas