Can one have blind belief in Allah SWT meaning that they can not prove it rationally or logically, if so please provide references?
Proving one’s belief rationally or logically is a contradiction, as belief is by definition in what lies beyond the probative power of reason and logic. However, if you mean by “blind belief” ignorance of its proofs – or most of its proofs – in the Shari`ah, then that is the position of the “general public” (`awamm) of the Muslims and belief is not harmed by it, although it is probably incomplete or weak and definitely more vulnerable than the belief of the `alim. Hence Allah Most High orders us to seek strong and discerning faith with the command “Know / Learn / Understand / Realize that there is no God except ALLAH”. Similarly the responsibility of the `alim is greater and his sin weightier. May Allah forgive all and guide all.