The key here is to understand exactly what "witness" means in this context.
According to the Theological Dictionary of the New Testament, "the concept of witness [is used] both in the sense of witness to ascertainable facts and also in that of witness to truths, i.e., the making known and confessing of convictions." So a witness relates facts from direct personal knowledge, or he proclaims views or truths of which he is convinced.
So a "Witness" is someone that speaks publically about what he knows to be true. Of course no human has ever literally seen God (John 1:18), but Jehovah's Witnesses realize that God has asked his faithful servants to be His Witnesses and to tell others about Him:
"Ye are my witnesses, saith Jehovah, and my servant whom I have chosen;" (Isa. 43:10) - ASV
Isa. 43:10 also corresponds with Acts 15:14 where it says that God will turn "his attention to the nations to take out of them a people for his name." NWT
According to the Bible, the line of Witnesses of Jehovah reaches back to faithful Abel. Hebrews 11:4-12:1 mentions this line as a "great a cloud of WITNESSES surrounding us."
The Bible says that Jesus Christ was the foremost witness of Jehovah: "These are the things that the Amen says, the faithful and true witness, the beginning of the creation by God." (Rev. 3:14) Considering the definition of "witness" mentioned above, Jesus said that it was his Father's name that he made manifest. (John 17:6)
For more, see:
Why Are You Called Jehovah’s Witnesses? (JW.ORG)
What Does it Mean to Be a Witness For Jehovah? (Defend Jehovah's Witnesses
How We Came to Be Known as Jehovah’s Witnesses (Charles Taze Russell and the Watchtower Society)