That is a very good question. Please allow me to offer this by way of an answer. Scripture reveals God operating in three distinct functions. These three distinct functions involve intelligent design, active cause, and organization. I prefer to use the idea of triadic position to show the functional relationship that each appears to have with the other members and to define the role that each has within the triadic structure.
The First Position, that of the Father, will always appear as the one who represents the idea or the planning. It is also the position of command. The Second Position, the Son, always appears to be the avenue of communication between the natural world and the unseen world. He also serves as the causative agent. He is always the one who gives substance to the idea. He takes what is abstract (the idea) and gives it form and substance. The Third Position, that of the Holy Spirit, will always serve as the linking agent. He is the one who brings order to the work of the Second Position. He organizes the work of the Second Position so that it conforms exactly to the idea of the First Position. He shapes a finished product.
The positional functions of each appear to be somewhat exclusive. In all of my studies in scripture, I find it quite rare that one member of the Triadic Unity is ever seen operating in the function of another member. For example, we never seem to find the Third Position functioning as the active cause or the Second Position functioning as the linking agent. Each member of the triadic unity always appears to function within the parameters of his exclusive dynamic. There are places where some of these may appear to overlap but this does not change the basic parameters of positional function.
As the agent of communication, the Son always seems to be the one who serves as the conduit between God and man. If this is true then any time we see communication between God an man, it almost alway seems to be through the agency of the Son. The only exceptions I find in scripture where this is not the case is at the baptism of Jesus and the command of the Holy Spirit in Acts 13:2 where he says,
“Now separate to Me Barnabas and Saul for the work to which I have
It would seem then that all theophonic manifestations recorded in scripture always represent to appearance of the second position of the triadic unity. So, I would suggest that the one who is spoken of as walking in the garden with Adam would have to be the pre-incarnate Son.