Let's start by answering all four questions, and we'll look at the actual meaning of the title.
What is the meaning of 大兵小将 , character by character?
大 means big when looked at alone, however in this phrase, it also has the meaning of important
兵 means soldier
小 means small, but in this phrase, it also means unimportant
将 means General(将领) like Tang Ho said
What is the "will" character for?
It's for 将领. (This 将 character has two pronunciations, one of them means "will do something", the other means "commander/General". In this title, since it's used with "soldier", we'll know it's taken the latter.)
Why are "little" and "big" on different sides of "soldier"?
The "big" is for the 将, not for soldier.
Isn't "Big Little Soldier" translation as correct as "Little Big Soldier"?
Yes. But this is not relevant to this movie title (given the correct translation).
Then what's the correct translation?
First we need to know that there's a traditional phrase 小兵大将, using the exact character by character translation above, we get "unimportant soldiers, important General". Made more readable, it becomes "(In the field,) one good General is more important than (the number of) soldiers."
This phrase is used to emphasize the vital affects a commander will have on a war.
With this in mind, we look at 大兵小将, which is the reverse of 小兵大将. The main character in this movie (Jackie Chan) is a soldier, so this title is a twist of the traditional phrase, meant to emphasize that "soldier(Jackie) is also important".
Last bit of information: popular movie/song/shows sometimes use something derived from slang/proverbs/ancient stories, and it can be hard for Google to translate the correctly. (Similar example in English: Zootopia -- Utopia)
Hope this helps!