I have never tried this but if you'd like to implement AP mode on your Galileo, you would first have to check if your wireless card supports IEEE 802.11. If it does, it might be compatible with hostapd, in that case I'd suggest you to read https://w1.fi/hostapd/. You might also be interested in checking Edison's hostapd configuration (in case you have access to an Edison), which can be found in /etc/hostapd and /lib/systemd/system/hostapd.service.
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steps may be, for example, like this:
Edit hostapd.conf as needed Configure DHCP server (like udhcpd) # systemctl stop wpa_supplicant # rfkill unblock wifi # hostapd -B /etc/hostapd.conf # udhcpd &