Given that the LEDs are backwards in your schematic, leads me to believe there maybe some things that are different between the schematic, the PCB, and whats soldered on it, making debuging harder. And the fact the LED is lit means you've clearly soldered it correctly, but it does create doubt.
I did a quick google of SSD1306 board schematics and yours and they look identical. The obvious thing to check is runa multimeter across every LCD connection to make sure its as it should be, they it would be running a logic analyzer on the I2C lines, or better a scope, just to see what the edges are like.