Hi Chris,
if I see this correct on the Picture, you did connect the LED data to D2 (that’s GPIO9 on this particular board) but you need to connect it on the other side on p the pin labled with “2” (that’s GPIO 2).
Then I’m not sure if the 2nd pin from left (next to the 5V pin) is really connected to Ground - there are several versions where this is the “CMD” pin (for flashing purposes).
So you could try to use the 6th pin from the left - this is definetely a ground pin.
And: yes, you do not use a capacitor yet, but you SHOULD
In some cases a 47 uF tantal capacitor is enough, but I recommend using a 1000 uF electrolyth capacitor (be aware that you need to connect “+” to “+” and “-” to “-”).
ESP8266 are not that “choosy” when you connect them to an external power supply, but ESP32 are.
So use a “big” power supply (no phone charger or something similar small).
That should work …