a circuit output is going to drive the next stage circuit which is a large capacitive load of the previous stage(please see the simplified picture below)
In order to drive this large capacitive load, should I consider about increasing the current flowing in the previous circuit or should I increase the size of the transistors Q1 and Q2?
In general, in order to drive a large capacitive load, how can I optimize the circuit?
If you are driving the capacitive load with an inverter which is seen from your schematic, rather than using a single inverter use chain of inverters namely "tapered buffer".
U will have to increase the current and correspondingly the size of transistors also, which will increase the input loading of that stage, u may have to add another stage before that to run it.
2 or 3 stage buffers can run a large capacitive load.
Hope this helps.