Logical Contradictions?

If I posited that such a thing as a "square circle" exists, how would I prove or disprove its existence?
Well, first, I would refer to definitions of a square and a circle, and as such, that geometry renders them as distinct non-like concepts/shapes.
Here is a definition for "Square" - from : Dictionary
Definitions from Oxford Languages

• "a plane figure with four equal straight sides and four right angles"

​Here is a definition for "Circle" - from : Dictionary
Definitions from Oxford Languages 

• "a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)"

Rendering on paper geometrically makes it known that the two manifestations "look" different, and one is compelled to say, "these are distinct objects that are not the "same" thing.
Is that good enough for a "proof"?
Well if not, then we could introduce the rules of logic and in that context offer proof that a thing cannot be an object/concept and a different object/concept at the same time, a violation of the principle of "identity".

So, what to make of a "Square Circle"?
In logic terms, this is a contradiction, and to then carry on describing this thing and referencing your belief towards it is an attempt to change definitions and assigned properties.
In short, a defense of nonsense.

Within the paradigm then, definitions emerge as "truth statements" or "truths to the Universe", a concept very much in debate and controversy in our modern culture.
Some go on to infer that even God could render a "square circle" if "He" wanted to.

I believe this last statement is where the whole system of "truth" breaks down.
Even God cannot operate contrary to "truths to the universe".
Something to ponder, even before the "big bang", or whatever mechanism gave rise to creation, did the concept of a square exist somewhere in form waiting for a universe to come forth and claim the concept of "square" for use in i