You can get a lesson straight away but you must do this by why getting the teacher to invite you. So you would need to message the teacher to ask if they were available and if they were willing to invite you for an "instant lesson". Just check the teacher is online first by looking at their profile page to see if there is a green dot indicating this status.
I found this on the iTalki website:
"If you and your teacher have agreed to an instant lesson, your teacher can use the Lesson Invitation feature to send students a lesson request to start a lesson within 15-30 minutes. After you accept the lesson request, you can start the lesson soon!
Note that your lesson is only booked when a lesson request is accepted."