Commas After Introductory Phrases
An introductory phrase is like a clause, but it doesn’t have its own subject and verb; it relies on the subject and verb in the main clause. Unless the phrase is very short (fewer than 5 words) and begins with a preposition (to, for, at, etc.), there should be a comma between the introductory phrase and the main clause. You can use your own judgment here: if you were saying the sentence out loud, would you pause after the introductory phrase?
Fighting against reason, Martha decided to pull an all-nighter in hopes of passing the exam.
Without understanding why, Annie woke from a deep sleep with an urge to check on her children.
Between March and April, the little boy grew three inches.
By flashlight we made our way along the path.
Because the introductory phrase by flashlight is short and begins with a preposition, a comma is not required; regardless, it wouldn’t be considered incorrect if there were a comma after flashlight.