You can't speed up the process by sending it to the pre-school.
It's part of the tamas evolution. It goes to pre-school first and then to school.
Doesn't matter if you send it to pre-school 10 times or 3 times, you will still wait the same amount of time for the [!] letter to graduate.
The difference is in the skills points. Each time you send it to pre-school you have the chance to earn more skills points (in random categories - you can't choose).
So if you never send it to pre-school you will graduate to the elementary school with a lower number of skills points.