Ok,
It's difficult for me to understand what the term "warm" means to you but I took another listen, and I want to modify my original statement.
I think that first pad can be emulated with a saw wave going thru a ADSR. That's what, I think, may be described as the warmth. Maybe?
The saw wave emulates the timbre of a horn section... imagine a horn section playing quietly when that songs starts off and see if that makes sense to you.
The ADSR is used to make the initial transient smooth and pad like rather than percussive like a piano.
It seems like a strings type pad is layered on quickly after ward and they play against each other in anticipation of the wood wind and organ joining in.
best regards,
mike