Astable multivibrator: what starts the first cycle
First, at some point the power must be turned from on to off.
Second, in the real circuit the capacitors won't be exactly 10.000 uF (or exactly equal to each other) and the collector resistors won't be exactly 47.000 kohms (or exactly equal to each other). (And the BJT's won't have exactly the same \$\beta\$ and the LEDs won't have exactly the same forward voltage, etc.)
The imbalance between the component values on the two sides at start up will produce a slight difference in which BJT gets turned on first, starting the oscillation.
To see the start-up behavior in the simulator, you will have to tune one of the circuit parameters slightly off (maybe 1 or 2%) and simulate the transient when the power supply is ramped up from 0 to 9 V.