Can we stop thinking too much?

The stopping of thought should not be the focus of meditation. It is possible that this happens though, Buddhism calls this samadhi, I think the same applies to Hinduism. When the mind enters (deep) samadhi thinking stops. There might be some small notions remaining, yet these won't classify as thinking. And when those notions stop there will be nothing left that we can classify as thinking at all. The practice itself leads to samadhi when done right, the mind will move into samadhi when it's ready.

Once the very deep meditation with no thoughts has happened once it will be possible to (at least for a while) switch focus to enter a state of mind without thoughts. A quick recollection (and by that time you will instinctively know what this is) is sufficient.

Yet this is for now a distraction. The practice is rather easy. Dig into the meditation object and view it, contemplate it, don't lose it from sight. Then you will come to know the object and also the nature of mind that is 'observing' the object. When you get skilled at this you will find that the object and mind are more and more seen as one and this will switch the focus of meditation from the object to the quality of observation. You should not force this, when you meditate keep attention on the object. The shift to mind will happen when you do this (so no following thoughts, accepting what is present or something like that: work on the object).

When attention shifts from the object to the (quality) of mind, this will cause some disturbance. It's this disturbance that will reestablish the meditation and where afterwards the mind will have full focus on itself with the meditation object as secondary point of awareness (it will be 'spinning' by itself, so to speak). It is from this state of mind that the 'silence' might emerge. The mind will know it's nature in relation to the object and based on this insight will be able to let it go. When it let's go what remains is samadhi. When the thinking and notion aspects of meditation stop what remains is a form of awareness without notion and without thinking.
Don't think that 'you' can start or stop this process, the controlling 'you' will be long forgotten in such a mediation.

Keep focus on the object, over time become sensitive to the movements of the mind and with this the mind can shift from object to self observance (in relation to the quality of observance of the object). This is the way to practice, samadhi should not be the goal.

Also and I'm going to be a little harsh on this: meditation is an activity. Sitting silent observing thoughts is letting things happen. This seems lofty yet it's not what meditation is about. Meditation is closely linked to mindfulness. Mindfulness is the Pali word 'Sati'. Lucky this word is still used in Thai and it is used to keep your attention with something. No sati = you lost your head. If you allow all kinds of thoughts to pop up and be indifferent about the thoughts, this is stupid. It's like seeing that your toilet is jammed and not acting. You should get your gear and start working to get the shit out!