Keyless entry - 2006 Sequoia

Hello,

After working on my car a bunch, I came to a point where the exterior looks really nice (new rear bumper, and fender flares, polishing...), and the car drives perfectly now.

So I'm starting to find new ways to improve it.
In this case, I'm trying to have (or reactivate) the keyless entry on my car.

It's a 2006 sequoia SR5, and I know that AT SOME POINT OF ITS LIFE, this car had keyless entry (here is an add I've found with my VIN, of my car sold by a dealership https://samsdiscountautos.net/vehicles/821149, you can even see the keyfob hanging on a picture, and it's listed in the description).

The thing is : I only have 1 key now (+the emergency unlock key) and no keyfob to open it from outside.

What can I check to know if the keyless entry module is still present ? And should I go to a dealership to get a new key + keyfob and a programmation?

I have tried to make it enter programmation mode, but the car just doesn't want to (all my actuators are working great, all doors opens and closes fines).

Thank you for your help,
Clément