The clock starts at approval
Not when you first call. Not when you send the file. The one to two weeks starts the day you approve the mockup and the sizes, because that is when the shop can actually start building your job.
Order two to three weeks ahead
Two to three weeks ahead is comfortable for most bulk runs. That leaves room for a mockup. It leaves room for a change or two. And it leaves room to print without anybody sweating the date.
The weeks everybody wants at once
Football kickoff, playoffs, graduation and elections all land in the same few weeks. Every group in town wants shirts then. The earlier your order lands, the safer your date is.
Rush orders
A rush can be done. It costs more and it depends on what is already on the press that week. Call and ask before you count on it, and bring your real deadline to the first conversation instead of the end of it.
Bring the date up front
If you have a hard date, say so on the first call. A deadline is treated as part of the order, not as a hope. The shop would rather tell you no early than miss your event.