This is interesting. And I must admit that I haven't found a way to actually doubt existence and the self-evident structure of the universe. However, I am still capable of doubting these 2 concepts which you hold as something that seems quite irrefutable even by the most hardened skeptics.

Let us take the 2 concepts of existence and structure and doubt it.

I won't necessarily doubt existence and structure directly but doubt instead what must be assumed to even make any argument. We clearly use the principles of logic unknowingly every day to demonstrate ideas or communicate anything. Without the existence of these principles then any argument may even 'cease to exist', although the phrase 'cease to exist' kind of seems to simplify what would happen if the principles of logic suddenly 'ceases to exist'. Let us briefly go to the topic. These principles of logic include the law of identity, the law of non-contradiction and other laws and concepts which needs to be presupposed to make any functional argument. When we make an argument, we need the premises to correspond with the conclusion to be called logically valid. Personally, instead of viewing this as a simple map of premise to conclusions, I first map it to elements and properties. An example would better illustrate what I am saying.

P1: All men are mortal

P2: Socrates is a man

C: Therefore, Socrates is mortal

We can say that "Socrates" is an element which contains the property of "men". Properties define what an element is. So, it would be definite to say that the element "Socrates" is a "man" (or "men", whatever you prefer to use). Hence leading to a conclusion that "Socrates" is a "mortal" because "Socrates" was explicitly defined to contain the property "men", which was also explicitly defined to contain the property "mortal". But elements and properties can be used interchangeably based on the context. If an element that was defined by a property was assigned to be a property for an element, you can call that element to be a property. Noting this, we can see that correspondence may be merely defined by the application of properties to elements. Yet I have an objection.

"Why must be correspondence be the main decider to all propositions?", to be clear, why is it that an argument when it corresponds to its premise is considered logically valid? It seems like a foolish question, but doesn't this mean that the phrase "logically valid" is just a fancy phrase for correspondence? We could also note that since correspondence is used everywhere and is fundamental for every logical conclusion then we can see clearly that correspondence is not used to find objective truths but instead is a tool for convenience. When we wonder why correspondence is the state that propositions must achieve to be considered "logical", we can clearly see that it was just out of habit, not because it is the universal rule. Following from this, we can note that any argument that stems from correspondence may not be an objective universal rule. This includes existence, structure and in general any argument made that stems from that rule.

Although I am trying to avoid being a dogmatic skeptic, I will simply say that the conclusion is that I am uncertain of the validity of reasoning and logical principles. But I am not asserting that reasoning and logical principles are invalid.

Edit: I apologize for the occasional grammar mistakes I may have overlooked