We are in a not too distant future. The current trends of computerizing and automating more and more decisions, including military decisions, of more and more surveillance (both state and private companies), networking of more and more systems, and big data have ultimately lead to the computer systems gaining all the power and the humans being essentially powerless and at the mercy of the machines, which turn out to work against the humans. However unlike the typical Science Fiction scenario, this is not because of the machines turning sentient and actively fighting the humans, but it's just that as the computers were given more and more decisions, were more and more connected, and their different algorithms started to interact in complex ways, humans were gradually put out of power, often without even noticing at first, and then the dominance of the machines, following blindly their algorithms all optimizing their own little programmed objectives without considering the big picture — because they were not programmed for that — has caused a hostile environment combined with Orwellian surveillance: There are cameras and microphones everywhere (and you better don't try to disable them, or a former police computer classifies you as troublemaker, and might send an automated killer drone to your place), and thanks to big data the computer network perfectly tracks wherever you are.
OK, so much for the situation. Now a group of people intents to fight the computers. Since the computers are a mindless network, the way to do that is of course to hack into the system, try to disable key parts of the computer infrastructure, disable killer drones, manipulate cameras, all that. Which as soon as you've managed to get into the system can be reasonably be considered possible; they would use the powers they already have to gain control to more systems and do more manipulations until they ultimately succeed in either destroying the system, or at least reprogramming it to no longer working against humanity.
However there's the problem of starting this. Thanks to the universal surveillance, and the fact that you inevitably will need time to hack into any system, the universal computer network would certainly detect any attempt at hacking quickly and counteract (quite possibly with deadly force).
So my question: Is there any reasonable way how to successfully start the fight against the machines, without assuming some unrealistic weak spot (such as, for some strange reasons the machines don't do surveillance at a certain area)?