possibly

möglicherweise

Perhaps; indicates that the proposition may be true (is not certainly false) regardless of any facts or circumstances known to, stated by or implied by the speaker

• How could Tom possibly know that?

  Woher konnte Tom das nur wissen?

  Tatoeba · CK · CC BY 2.0 FR

• How could I have possibly known that?

  Wie hätte ich das wissen sollen?

  Tatoeba · CK · CC BY 2.0 FR

möglicherweise

In the realm of possibility; indicates that the action may successfully be performed (is not impossible) regardless of any facts or circumstances known to, stated by or implied by the speaker that might limit the performance