I know this is an old thread, but it came up in a duck duck go search for me, so it probably will for someone else also.
I had the same problem with the bcm4313, saw this thread, and cursed a bit because I really didn’t want to have to hookup a cable. But I thought it was odd that there was a thread from an OLDER Antergos iso version where someone was complaining that the same chipset was working in the live environment but not on reboot that led me to think it should probably also be able to work on the updated live environment - so with a little more digging I found an Arch forum thread where they recommended manually loading the brcmsmac module from a terminal window in the live environment. Sure enough it worked.
So just one command from within the live environment.
sudo modprobe brcmsmac
Then I could see wireless networks in the system settings and was able to connect and install. I should add that it continued working and saved my wifi settings post-install.
From the Arch Wiki:
If your card is in the following list, you can use the brcmsmac driver:
The brcm80211 drivers have been included in the kernel since 2.6.37. Since the release of 2.6.39, they have been renamed to brcmsmac (for PCI cards) and brcmfmac (for SDIO).*