Does "By April" imply a particular date in April?

What does the phrase By April mean in this sentence?

By April 1857 the army had grown to approximately 700 men.

Does it signify before the end of April or at the beginning of April?

The author is counting by months. April is not only a period of time, but a counter of time; here you are counting time by months; thus the discrete unit of time is not meant to be broken down. Here April means the month of April in its entirety. It's like counting by 5s: 5, 10, 15, 20, 25. There are no units in between and there is no conception of at the beginning of or at the end of 15 (for example).

I would always take such a statement to mean by sometime during April or before April was out.

Had they meant before 1st April, or by some date in April, they would have likely said something else, such as before April 1857 or by 12th April 1857.