Hi,
The short answer to your question is that we can't change the fundamentals.
The long answer would be...
The process of checking if two objects are touching each other in game dev is fundamentally known as 'collision detection'. Because they are one of the primary pillars in game dev, most engines have built-in systems to do these tasks.
This means, if your intentions are NOT to use colliders and rigid bodies then you will have to do it manually, i.e make your own little systems through coding (or combination of Playmaker Actions) to detect collision which depending of the shape of the objects involved, is either simple trigonometry or complex calculus formulae.
There are tones of papers, tutorials and resources available for this. The engineers have gone through all of that and made colliders, rigid bodies, physics simpler to work for people like us who do not like to get into that much technicality.
So I am afraid you would have to asses how unique case scenario is yours and is it really worth doing all that work to detect collision manually. Perhaps there is a different approach to the solution or there is a different approach to the design itself.
Having said that --------------------------------------
I can suggest one way if you must absolutely avoid using colliders and rigid bodies on your main game objects.
Perhaps you can create proxy objects for each of your main objects. Those proxies can sit anywhere in the game so that player cannot see them. Use all your colliders and rigid bodies on those proxy objects and perhaps setup a feedback system that can in turn control the main objects (may be parent-child relationships).
Think of it like a steam valve that you want to turn without touching it coz its too hot. You would may be use a piece of cloth to grab it, or use a crowbar to twist it. The cloth/crowbar can act as a parent to the valve. The colliders exist on the cloth/crowbar but not the valve.
Don't know if that jibber jabber makes sense...
-peace