First, the Constitution does give the deciding power to the SC. I refer you to Article 3, Section 2.
What you are saying is that the founding fathers, the men who wrote and enacted the Constitution, did not agree with your interpretation.
No, I am saying that the writers of the constitution failed to designate in the constitution that the Supreme Court was to decide the constitutionality of laws, acts of the congress, states or the executive. The wording for that power is simply not in the constitution. The Court under Marshall decided that in the most famous court case, Marbury v. Madison.
I again refer you to Article 3, Section 2. It is not unclear. "The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution,..." Marbury simply clarified that language, it did not create the authority.
As one of the primary FFs, Hamilton, said in the federalist papers:
The courts were designed to be an intermediate body between the people and the legislature, in order, among other things, to keep the latter within the limits assigned to their authority. The interpretation of the laws is the proper and peculiar province of the courts. A constitution is, in fact, and must be regarded by the judges as, a fundamental law. It, therefore, belongs to them to ascertain its meaning, as well as the meaning of any particular act proceeding from the legislative body. If there should happen to be an irreconcilable variance between the two, that which has the superior obligation and validity ought, of course, to be preferred; or, in other words, the Constitution ought to be preferred to the statute, the intention of the people to the intention of their agents.