The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
I see "probable cause" and specificity ("Oath or affirmation"). I do not see notice required. One can at best infer notice from the above concepts. Ordinarily one can cross-examine oath takers, but would have to know about the oaths in order to do so. Naturally this is impossible before the search, but can be used to quash evidence at trial. And indeed, at trial one gets notice of evidence and can attempt to refute the evidence or even have the evidence thrown out by refuting the probable cause used for the warrant.
I don't see notice or refutation either implied or necessary before the government does something with the evidence at trial; for one thing, at trial one can at best get the evidence thrown out of the proceedings; one can't undo the search.
In sum:
1) One virtually never gets notice before the police come to your door to perform a search (lest you remove evidence).
2) If there's a warrant, the search will be made whether or not you're at home, and regardless of any objections you might voice.
3) Before the government can do anything against you with the evidence, you can contest it and the warrant at trial, and have it thrown out. So you have notice and can contest before the government actually does anything with the evidence.* Provided you are given a reasonably speedy trial, and are given information about the search in sufficient time before trial, none of your rights have been violated.
* anything legally, that is. The government may of course use the evidence to track down illegal combatants in our war on Islamofascist Terrorism. But that's exactly the point.