The only way to determine if laws are constitutional is for an issue to be brought before the court in the form of a lawsuit. So if no one sues on the grounds that a law is unconstitutional, how would we get a ruling? Unless of course you are suggesting that the Court sit down with a copy of the legal code and render an opinion on every single law?
No. That's not the "only" way we can determine that a law is unconstitutional.
If Congress for some ridiculous reason passed a law that said no white person (or no black person, it really doesn't matter which one for this silly hypothetical) would be eligible to serve in the nation's armed services -- or would no longer be permitted to vote in Federal elections unless they brought property tax receipts -- it would be a good thing if the President made a determination articulated in his veto message that the act was unconstitutional. He can do that, you know.
Now say that the idiot Congress overrode the veto. Then the President might simply REFUSE to enforce that law or permit anybody in the Federal branch to give it ANY effect.
NOW we might have a court battle looming. The jerkoffs in Congress MIGHT sue to compel the President to enforce the law, but the President might get the Court to dismiss the lawsuit on the ground that the bill is Unconstitutional. The point is, that whole "go to the SCOTUS" thing is not the only way to determine that something is a violation of the Constitution.
Hell. For that matter, if the SCOTUS were to determine that the Congressional act DIDN'T violate the Constitution, does anybody REALLY think that the obviously and facially unconstitutional Act is somehow now made pure and wholesome and Constitutional?