Mind and Muscle
Note: as I'm not a MOBA player I can't really advise you too much, but I have included facts that I hope you'll find useful in this section.
The mind tells the body what to do, and the muscles react instantaneously, more familiar the mind and body are the faster the movement will become.
The same principle applies in gaming, the more you play, the more you will become familiar with what you're doing and your muscles start to have natural reflexes. Your reaction time is important, but you also need to develop muscle memory... What is muscle memory?
Muscle memory has been used synonymously with motor learning, which is a form of procedural memory that involves consolidating a specific motor task into memory through repetition
With that, you need to aim your cross-hair as quickly as possible on to your enemy's head, to maximize damage or at least on his body, the more you do it, the more your muscles will react with speed precision.
Train vs Bots
In CSGO, and the same in Overwatch, there are some custom settings that you can apply to the enemies bots in order to make it more challenging. Selections such as, head-shot only, with or without enemy movements, spray control, increased enemy health and so on.
Using these options everyday, for at least 30 minutes, will improve your aim considerably.
There is another software program that I personally use for the last month before entering in to the game, you can find the software here (I suggest this for Overwatch players, the workshop maps for CSGO are as good), there are Overwatch, CSGO and even Paladins and Quake sensitivity settings in the options.
I use it for 20 mins before going in game, and take 30 mins with bots, only after all this I will start to play.
Find your sensitivity
There are so many posts around the web about this argument, "playing with low sens is the best" I can tell you, this is wrong.
Of course avoid playing with super high sensitivty, as it becomes hard to get track of where you want to aim, but it's all about practicing, there are so many pro players that play with what is considered high sens but perform incredibly well.
Get used to your mouse speed and stick with it till the end, don't keep changing it thinking that maybe if you lower it, it's better.
If you're interested here the setting I use to play:
CSGO: 400DPI, 2.7, 6/11 windows
Ovetwatch: 800DPI, 4.5, 6/11 windows
Meditation can help you to focus before a game, I don't know if you have ever meditated before, if you never have, it's better for you to follow a tutorial online, because I find meditation really powerful for gaming, as it calms your mind and focuses you on your goal.
When should I meditate?
You can start to meditate while you're searching for a game, or if you wish you can stop everything for 5 minutes and then go for the game. If you're asking yourself if I should do this? The answer is yes, at every game.
I read a long time ago about a gamer who used a stone to keep himself focused on every game just by touching the stone before a game and at every death... the name of the stone is Carnelian (I don't know much more about it)