How can the sentence starts with "with"? I have looked at the sentence following this part, but still don't understand the role of "with" here.
"With" in this context is a preposition, and is used at the beginning of the sentence to give more information or reasons for doing something. Starting this sentence with the preposition "with" is grammatically correct, but makes the beginning of the sentence a dependent clause and requires another component to complete the sentence. It is common to start sentences with "with", however, it makes the sentence less formal. Ex: With the pandemic keeping people indoors, many small businesses have gone bankrupt. Ex: With ten kids, she is already very busy.