Since the design and construction of skyscrapers undoubtedly reflects a human impulse to equate bigger with better, these buildings do, in fact, create opportunities for ingenious problem solving.
Let's simplify the sentence: Because the design and construction of the skyscrapers reflects a human impulse to equate
bigger with better, these buildings do create opportunities for ingenious problem solving.
1) 'Since' = 'Because'
2) Second thing that I noted was the article 'the' before the compound subject 'design and construction of skyscrapers'. This definite article along with the meaning of the sentence suggests that the compound subject is a singular entity and thus usage of singular verb 'reflects' is justified.
3) So, the D&C of S reflects a human impulse for what?
- To equate bigger with better. (Notice infinitive 'to' to showcase the purpose)
Now, Equate X with Y, Equate X to Y, Equate X and Y all are correct idioms and it depends how we use them in the sentence.
e.g. Many people seem to equate GMAT with GRE.
e.g. Please don’t make the mistake of equating high GMAT scores and intelligence.
e.g. You cannot equate the sins you do in this life to those you did in your past life

All the sentences are correct. All the above idioms are used to show similarity between X and Y.
Coming back to the original sentence: Since the D&C of S reflects a human impulse to equate bigger with better.
We have a subject and a verb therefore it's a clause. Since it was started with a subordinating conjunction 'Since' we can say it's a Dependent Clause.
Now what are we equating?
-Bigger and better?
--This is just a figure of speech.
Example: Car Dealers still think that the Americans equate bigger with better.
--This means that the Americans think the bigger the thing is ...the better it is. Big Car = Better Car.
So the meaning of the Dependent clause till now is: The Design and construction of the skyscrapers shows the human impulse of comparing big buildings as better buildings.
Moving on to the next part of the sentence: "these buildings do, in fact, create opportunities for ingenious problem solving"
This is an Independent clause (Subject: 'These buildings', Verb:'do create')
Meaning:The Big buildings actually create opportunities for ingenious problem solving.
Overall: DC,IC structure
Overall Meaning: The author is saying that even though it's a human impulse of comparing bigger with better, this impulse is not a bad thing after all. The bigger buildings has created opportunities for ingenious problem solving.
Coming back to the statement:
It's not because D&C of S reflects a human impulse to equate bigger with better, the buildings create opportunities. There is no cause and effect here.
The first part i.e. DC is a premise for which author has not provided any evidence , the second part (IC) is the main conclusion of the argument

Therefore we need a coordinating conjunction 'But' to show the change of thoughts and to join two clauses.
Ex:
--The high sales of the new model of rolls royce show that people consider the bigger car as better car, but the new model of rolls royce, in fact,has many advanced features.
A) Since the design and construction of skyscrapers undoubtedly reflects a human impulse to equate bigger with better,
--Incorrect.
B) While the design and construction of skyscrapers undoubtedly
reflect a human impulse to equate bigger with better,
--S-V error
--Usage of while is correct. It's not a adverbial of time here, it's used for showing contrasting ideas.
C) The design and construction of skyscrapers undoubtedly reflects a human impulse to equate bigger and better, but
--Correct and it matches with our understanding.
D) Although skyscrapers’ design and construction undoubtedly reflect a human impulse for equating bigger and better,
--Use of subordinating conjunction 'Although' is correct
--Use of possessive form of noun is not incorrect. (skyscrapers’ design and construction) however, the problem is again S-V error. The subject 'Skyscraper's design and construction' is again a singular subject and it need a singular verb 'reflects'.
E) That the design and construction of skyscrapers undoubtedly reflect a human impulse to equate bigger with better,
--Run on sentence