Have you ever tried the whole thing without the display? So only connect the Pi and the sound card and nothing else. In addition, you could try disabling the „Autostart Desktop“ on the Settings/Reboot page. Does it work then? Have you also tried changing the Squeezelite audio output? Please select
sysdefault:CARD=ALSA – bcm2835 ALSA, bcm2835 ALSA – Default Audio Device and connect headphones to the jack input on the Pi.