There are experts here that know more than I do, but we just drove it the other way, from Guayabo Lodge to SJO back in April. Now we weren't in a hurry and the San Jose traffic was heavy and we made some stops along the way so hard to say how long it would actually take if you hurried.
But you have to deplane, wait for baggage, go through customs and immigration, maybe get a SIM card for your phone to use Waze, and then...are you renting a car? That's an hour just to do the paperwork.
So I don't think it's a good idea to try to get there after you land. Spend the first night at an airport hotel (we stayed at the Hampton Inn, right next to the Vamos rent a car office so very convenient, I would recommend them both.) That way, you can relax and enjoy the drive - once you get out of the urban San Jose area Costa Rica is full of spectacular views and interesting towns. Besides, you will be driving a lot on 2-lane roads that become one lane roads at times for short bridge crossings. Not a place you want to be driving in a hurry to beat the darkness.
Take a taxi to the other side of San Jose and stay at the Hyatt Place in Curridabat.https://m.hyatt.com/mt/sanjosepinares.place.hyatt.com/en/hotel/home.html Have your rental car delivered there the next morning and hit the road.
You could visit Irazu Vilcano or check out Cartago or do the route 224 loop around the Orosi Valley.
You could still arrive in Turrialba in time for lunch.