I assume you are trying to replicate Figure 14 in the TI LM555 specification that you linked. It is a sample circuit that allows "Astable Operation" or in other words, it self oscillates.
According to the TI formulas for Figure 14 (shown below Figure 15) it says that to have a 50% duty cycle RA should be 0 Ω. However, the 555 will not cycle with 0 Ω for RA; you must have some resistance.
I got my 555 cycling about 4 seconds on and 4 seconds off using 10 kΩ for RA, 330 kΩ for RB, and 22 μF for the capacitor.
Note: The TI formulas say my times should be closer to 5 seconds, but because of tolerances the resistors and capacitors values are not exactly what the manufactures say they are.
It doesn't look like you replicated Figure 14 exactly and that is probably why your circuit is not oscillating. I see that the 555 pins 2 and 6 go to both resistors as well as the capacitor. Pins 2 and 6 should go to the capacitor and ONE resistor. You show pin 7 going to one resistor; it should go to both resistors.
Since your 1 kΩ resistor goes to + I assume it will be RA and the 500 Ω resistor is RB. Your capacitor is 470 μf so the TI formulas would give:
t1 = 0.693·(1000+500)·0.00047 = 0.49s
t2 = 0.693·(500)·0.00047 = 0.16s
Obviously that is nowhere near a 50% duty cycle. To get close to a 50% duty cycle you are going to have to pick an RA that is insignificant to RB but is large enough to let the 555 oscillate.