While you can make an offer without being pre-approved/pre-qualified, chances are the seller either won't consider the offer or will counter back with that requirement. When representing sellers, I advise them not to accept an offer unless it comes from a ready, willing and able buyer. And, of course, part of being ready, willing and able is being pre-approved/pre-qualified.
It's not a painful process. All you need to do is just speak with a lender, fill out a loan application (can do this on line) and having them review what information you've provided. They will normally advise you that if all the info you've given them on the application is truthful, you are good to go - provided you have the documents to back up your income, job verification, debts, etc. and your credit score is within an acceptable range. At that point, they will provide you with a letter and state that based on their review, you are able to purchase the property with a caveat that the approval will be based on substantiating documentation, title search and satisfactory appraisal. Good luck!