I have not had any problem with first layer (have printed both on glass bed and on PEI coated sheet).
For the glass bed I usually use a thin layer of hairspray to ensure that part sticks, but the problem is usually the reverse. Have had parts that sticks so well to the glass that it chips…
If I print PET in 150% speed, I have noticed that some parts don’t adhere correctly. You could test if slower print speed helps. (on first layer)