How can I obtain a Will from 11 years ago that wasn’t put into probate?

First, if probate of the estate is finished, it is too late to do anything: probate closes out and ends the estate and also ends the period of time during which someone can challenge the proposed distribution, etc. of the assets. You indicate this is not the case, so you have apparently gotten over this particular hurdle--though an estate can probated and wrapped up without a will, based on "intestate succession," or the rules for who gets what when there is no will.
If probate has not been completed, you could in theory bring a challenge, though depending on if and when probate was first filed (i.e. has it begun), you may be out of time--there are statutes of limitations, or time limits on how long you have to initiate a challenge or legal action, to deal with.
Moreover, getting a copy of the will, which you would need, may be difficult or impossible: wills are not filed until probated, and there is no central repository for unprobated or not-yet probated wills. You'd have to try to get the will from someone, like your cousin, or your grandfather's attorney, or accountant, or perhaps a good friend of grandfather, who might have a copy. After 11 years, its certainly possible no one has a copy. Or they may have one, but refuse to admit they do. If you believe they have a copy but are lying about it, you could bring a lawsuit and in the lawsuit, use the processes of discovery (like "subpoenas") to "compel" them to provide copies--but we put "compel" in quotation marks because if someone has, say, the only existing copy but elects to deny he has it or even destroys it, and claims that he does not have it, there is likely no way to prove the contrary and he'll get away with denying its existence (after all, the court has no independent way of knowing if he or she is telling the truth, so if there is no separate evidence of the will's continued existence, somone could lie with impunity). You are describing a situation where there may be no way to take action as a practical matter.