In Minecraft, how can I light a beacon without using iron/gold/diamonds etc?

No

You can only activate the beacon with an iron ingot, or gold ingot, or diamond, or emerald.

This is like asking how to turn on a flashlight if you don't own batteries. Sh-t doesn't work like that.

Without mods, there are no alternatives to lighting a beacon.

You can't. That's part of setting it up.