Controlling which transistor turns on first in a multivibrator
I would use a C or an RC combined with a diode in one of the bases to influence the initial symmetry on startup. Once the C charges, the diode latches it out of the circuit. Maybe two diodes: one to the transistor base, and another one to discharge the C against the supply rail when you remove power (so that the circuit starts again reliably on short blackouts).

I would use a signal diode such as the 1N4148 (or if you have something yet finer, such as a transistor B-E circuit or a signal Schottky) so that it still functions as a diode against kiloOhm-range resistors in the base circuit, and so that its parasitic capacity doesn't matter in the timing.

Choose the C or RC such that it gets charged in a cycle or two of your circuit. Or maybe even a much shorter timing constant is enough to disbalance the circuit in the desired way.

BTW I got the very same idea and implemented a similar "threefold multivibrator" circuit some 30 years ago as kid. Only I guess I used some CMOS gates. Added some triacs (or was it relays? not sure) and used it to drive three sections of christmass tree lights on a spruce tree in front of our house :-)

===== EDIT =====

Looking at Mr. Tampieri's fine answer, I have another idea (I do not think this is what he suggests): use a trivial RC timing circuit to drive an extra transistor (a fourth T in the schematic) that briefly shorts one of the three vibrating bases to GND on startup :-) Once your RC cell (dis)charges, the extra transistor will go "open circuit" = vanishes from the topology. Let it be your homework to figure out how to connect the R and C to +Vcc and GND. The R will also guarantee a fast enough "reset" on circuit power-down.

Whether you use diodes or an extra transistor, my point is that the "bootstrap timer" vanishes from the circuit soon after startup, so that the symmetry of the three-fold multivibrator is not impaired during normal operation.