A search warrant is issued upon the establishment of probable cause. This requires that an affidavit or verbal affirmation be provided to a judge that meets that level of sufficiency, or, burden of proof. While actual objective evidence need not be produced at the time of the search warrant request, the burden of proof is upon the state to show that probable cause exists should it be challenged.
The two terms, "proof" and "probable cause," are not mutually exclusive, nor are they intrinsically intertwined.