Loose coupling, dependency injection, composition over inheritance, and similar techniques tend to be good answers to this question in my experience.
In contrast, over engineering attempts to solve tomorrow’s problems before they arrive and, if they arrive differently than predicted, makes them harder to solve, because when you have to change something it’s less clear which parts of the design were necessary to solve the original problem and which were only necessary for the future problem that was incorrectly predicted. Often times you might end up having to rethink the entire architecture rather than having the relatively simple problem of adjusting things to meet new requirements.
My own experience is that effort invested in removing restrictions and handling corner cases is generally well spent. It may not seem too onerous to have to remember that a particular function works only for nonempty inputs or when called after some other function, but in a large system where many operations have such restrictions, keeping track of them quickly overwhelms the capacity of human memory. Sooner or later someone is bound to forget, and it may even be the author of the code in question. I try to ask "what are people going to expect this code to do?" and then, if within reason, to make it do that (and failing that, to protect it with assertions). Alternatively, someone may be forced to make some other part of the system more complicated to work around the restriction, leading to excessive coupling.
I suppose this practice sometimes risks over-engineering, but I have found the risk to be worth taking. As you say, it makes the system easier to extend further.
To use inheritance as an example - if there’s a conceivable possibility that some future requirement might lead you to add the same functionality to other classes, you probably don’t want to have to deal with a long and convoluted inheritance chain when you could compose some set of functionality onto one class as easily as many classes.
Or in the case of dependencies, wrapping some third party mail sending library in your own generic API is barely more work than using the third party library directly and will pay dividends if you change mail providers in the future.
One very specific example that I worked on recently: In most cases there are one of X, but in a handful of cases there are many of X. My initial inclination was to branch off and handle the many case as an exception, but then I realized that you could eliminate that corner case entirely if you handled everything as a collection of X, even if in most cases that collection only has one item in it.
So, adding some extra architecture solves it?
For example, in Python, there's no need to go for a class when a simple function does the job. And once you do need a class, it's fairly trivial to swap one for the other, especially in a good IDE.
"Lean" tells you that small batches reduce the waste.
As an analogy, think about looking in front at the road that unwinds passing through cities and attractions until finally it becomes too small to see ahead. You feel that if you stay on the road, it will likely bring you to your destination.
Nevertheless you are not sure. As you move ahead it gets clearer were you are and where you will have to go.
So how far should you go before stopping?
It depends. It is all about how far you can see and how confident you are that it is the right road.
If you do not see too far ahead, it is probably a good idea to just reach the next city at hand and spend some time checking if you are on the right road. Otherwise you may waste time going too far on the wrong path. The further you go, the further you will have to backtrack.
But if you can see further ahead, you want to move faster and skip the pitstop.
This analogy only goes so far. But depending what you are building and were you are in process, and more importantly, how sure you are of what you actually need to build, you may less time in planning and just building what is merely necessary vs building a more complex architecture.
So you may say: "let's try to find as much we have to go and where before we start. But even the pathfinding activity takes time...
For me, I would rather put a bit of additional effort up front gathering enough information about the direction of the project or usage of it to better formulate an attack plan so that it does actually become more future proof. But even that is subject to failure, so what do you do?