This idiom or expression refers to:

An advantage (over others) at the beginning of a task.

We’re so confident in our team that we’ll give you a five minute head start. Go ahead. We’ll wait five minute before we start.

This idiom or expression has to do with:

Getting or giving help.
Getting or giving a head start.

A. You think he can do the report on his own?
B. Yes, but if you give him a leg up I would really appreciate it.