Of course.The father and the Son and the Holy Spirit exist at the same time.
But you have the Father as only one person that changes modes and thus ends up with the Father speaking to and interacting with Himself.
But they are distinct from each other and interact with each other.
The Father speaks from heaven (not the Holy Spirit or the Son) while the Holy Spirit descends (not the Father or the Son) while the Son is being baptized (not the Father or the Holy Spirit) by John in the Jordan River.