What is the transportation from Shanghai Pudong Airport to Suzhou?

Do you mean you will arrive at Pudong airport at about 6-8am or you will go to Suzhou from Shanghai at about 6-8am? If it means your arrival time at Pudong airport, I suggest you wait to take the first airport shuttle bus at 10:00 directly to Suzhou from Pudong airport. If it means your departure time to Suzhou, you can take the airport shuttle bus line 5 to Shanghai Railway Station and then take high speed train to Suzhou.

We will arrive at about 2am on PVG (at night).
Maybe we schould wait for the first subway?

After arrival at Pudong Airport at 2am, you could take the night line of Pudong airport shuttle bus transferring to Shanghai Hongqiao Airport. The journey is about one hour. Then, you could walk to the connected Shanghai Hongqiao Railway Station and wait for the first high-speed train departing to Suzhou at 06:00.
During the waiting time, you could stay at the terminal of the railway station, or one of these 24-hour openning restaurants.