In a word: yes. But there is a qualification: you shouldn’t do this too often. The reason is nothing to do with the words and and but themselves but with the group of words they grammatically belong to (coordinating conjunctions). As the name conjunctions suggests, the role of these words is to connect things and the things they connect are clauses (short sentences). The prohibition on using coordinating conjunctions comes from this use: if their role is to connect clauses, they cannot start a sentence, because then they are not connecting clauses but just introducing (most often) a single clause.
Like many theories, this theory does not always suit how we actually write. Sometimes, particularly for dramatic effect, it is fine to start a sentence with and or but. It is certainly much better to start with and or but if you mean and or but than to hunt around for a substitute word (the wimpy however is no substitute for a bold but). Remember, the problem was never with the words and or but but with coordinating conjunctions as a group (and and but just happen to be the most commonly used coordinating conjunctions). Other types of words do not always successfully work in the role of coordinating conjunctions.
How often can you use and or but at the start of sentence? In a short piece (not longer than one page), I suggest not more than once. In something longer, maybe once every few pages. If you find you want to start a sentence with and or but at least once in every paragraph, you probably need to think more carefully about your sentence structure. Remember, finding alternate words to substitute for and or but at the start of the sentence does not solve the problem and may make your writing less effective.
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