Can't lift head up for long

My baby is 16 weeks old, still absolutely hates tummy time and still can barely lift his head up when we are doing tummy time. He could last maybe 3 mins max of slightly lifting his head before he just shoves his whole face on the mat.

He has mild torticollis (no PT needed) and a really big baby. I am starting to worry that we only have very slight improvement.

When did your baby start lifting their head up?