Here's a breakdown:
Grammar: "Notwithstanding" functions as a preposition, and prepositions can indeed start sentences.
Style: While grammatically correct, starting a sentence with "Notwithstanding" can sound formal and archaic. It's more common in legal writing and formal documents. In casual writing, it might come across as stilted.
Alternatives: Depending on the context, you might consider alternative phrases like:
* Despite this...
* However...
* Although...
* Even though...
* In spite of...
Example:
Formal: Notwithstanding the evidence, the jury found the defendant guilty.
More natural: Although the evidence pointed to the defendant's innocence, the jury found them guilty.
Overall, while "Notwithstanding" is grammatically correct, it's often best to use more natural and less formal alternatives in most writing.