A recent article pointed out that well over half of four-year undergraduate institutions ask questions about criminal history (https://www.brookings.edu/research/thinking-beyond-the-box-the-use-of-criminal-records-in-college-admissions/amp/). Anyone who has applied for graduate school, a job, and/or a professional licensure knows to expect the same questions about criminal history in the application or certification process.
So does your prior criminal history mean that you don't have a shot at your dream gig? In short, it depends on how well you handle it. I'm often asked by clients how they must answer a particular application question for a job or for graduate school. My first response is always the same: answer only the precise question that you have been asked.
For example, if you are asked whether or not you have ever been "convicted" of a crime, then you should not disclose an "arrest" that never turned into a "conviction" (likely because of a dismissal or a not guilty verdict). Similarly, if you are asked whether or not you ever been convicted of a felony, then you do not need to disclose convictions for misdemeanors.
The more complicated scenarios involve: (1) when you are asked about convictions that you have had sealed or expunged; and, (2) when you are asked to disclose vague-sounding "crimes of moral turpitude" (common in professional licensure applications). These questions almost certainly require the advice of an attorney to answer properly.
The best defense against these questions is to have a qualified attorney have your criminal charge dismissed or significantly reduced before you encounter the questions. The second best defense is to know when you are required to disclose a prior incident. And the third best defense is to accurately and fairly report what you must---along with additional mitigating information to show that you are still a top candidate.
You should seek the advice of an experienced attorney in these matters before answering any application questions---it could make the difference in getting you the job or education of your dreams.