The definition of something now has account for its origins?
I thought you wanted a definition of what life IS, now you seem to want an explanation of where life came from. Entirely different question.
Well that would be nice, but not necessary if all one is asking for is a description of the principles involved in biological organization. The "how" question, not the "why" question.
Again, I aver a better definition is successful communication (Shannon) in nature.
Where there is successful communication in nature, there is life. When it ceases, there is death. And where it never happened, there is non-life.
"Purpose" in that definition is a matter of the message itself, whether to maintain, replicate, metabolize, organize, etc.
It is also mathematics, universal and holds up to intense scrutiny. And as a bonus it offends neither side of the ones who refuse to look any further: "nature did it" v "God did it."