The parameter which will influence take-off distance the most is weight.
The figures you quoted are take-off distances at MTOW. But if you reduce the take-off weight, you can use significantly shorter runways.
https://www.airbus.com/sites/g/files/jlcbta136/files/2021-11/Airbus-Commercial-Aircraft-AC-A320.pdf section 3-3-2 gives indications. Here's an example for an A320-200 with CFM56 engines:
As you can see, reducing the take-off weight as much as you can could get you down to about 1200m for take-off. But at sea-level, that means a take-off weight around 64t, 14t below MTOW.
At 72t (which is really quite close to MTOW), you'd probably be around 1600-1700m.
For reference, Gibraltar airport has only a 1776m runway, and still sees A320s flying in and out every day, and I'm pretty sure Easyjet doesn't fly theirs half-empty! That means they have to limit the amount of fuel, so probably no flying to Sharm El Sheikh from there, but the UK seems to be in range.
That's why BA's LCY-JFK flight using A318s stopped at Shannon (only in that direction): the short 1500m runway does not allow to take enough fuel for the whole transatlantic flight (the return flight JFK-LCY was non-stop as there was no limit on fuel taking-off from JFK -- though this was also partially helped by the jet stream). Remember that those A318s were all-business-class so also had a significantly lower payload than usual, which shows the importance of fuel.
Reducing take-off weight is probably the only reliable method of reducing take-off distance, so you can use it for scheduled operations. Other parameters are either intrinsic to the airport (nature of the runway, altitude...) or you have no control over it (wind speed and direction, air pressure...).
If the question is not about regular scheduled operations but rather a one-off event (e.g. "had to land on a very short runway in an emergency, how do I get out of there now?"), then you could indeed wait for some of the better conditions, but I'm pretty sure the first thing you'll do is reduce weight first. No payload, and just the amount of fuel required to get to the closest "normal" airfield. Only in the case that wouldn't be enough would one need to be more creative.