Question: Does eternal justification mean that a man is justified even before his existence?

Answer: Most definitely. It means that elect mankind is justified, transcendent of all human time, in the estimation of God in his eternal purpose. 

Justification planned: God determines to justify an elect people in Christ that he will create unworthy and sinful.

Justification constituted: Christ makes atonement for the elect in his perfect life, sufferings, death, and resurrection.

Justification declared: God and Christ publicly acknowledges each elect soul as justified by granting faith in the power of the Holy Spirit and simultaneously declaring the reality of their salvation in the heavenly courts (before the elect angels and deceased human elect)--as sure and certain.