Ok, I will give frictional contact a try.

I do have a version of this model with static structural analysis and bonded contact. The bonded contact, however, yields unrealistic results where the deformation only occurs at the outside and inside edge of the mask cushion, when really the mask cushion deforms and opens up in real life. I was hoping to use transient to get a more realistic result.

In my static structural analysis, there is an initial penetration of 1.8504 mm. Can I use that value in the Part Transform to adjust the mask to touch?