Jesus said, “Eloi, Eloi, lemá sabachtháni?” and was sinless, so did The Father abandoned Him on the cross, if so why?
I don't think so. For reasons we may understand only sufficiently rather than completely, God designed reality so that experiencing His presence is less than compelling and His grace is resistible, so that even Jesus (God the Son) on the cross cried out “My God [the Father], why have you forsaken [taken God the Spirit from] me?” (Matt. 27:46, Psa. 51:11)
This phenomenon is sometimes called “distanciation”, because we experience God as distant from us and “unknown” (Acts 17:23), even though He is close or immanent, “for in Him we live and move and have our being” (Acts 17:28). Distanciation is not forsaken.
Even if God were to prove Himself to skeptics by means of a miracle, they might believe for awhile and then as their memories began to fade they would probably think that God had died and revert to their former doubt (cf. Luke 8:13)—necessitating an endless string of miracles (recapitulating the story of the Israelites on the way to Canaan after the exodus from Egypt).
God’s normative means of conversion is persuasion rather than coercion (Matt. 12:39, 24:24, 1Cor. 1:22-23). This is seen very clearly in Jesus’ lament over the obstinacy of Jerusalem (Matt. 23:37). Two unusual theophanies included when God appeared to Moses (in a burning bush per Exo. 3:2-6), whom God wanted to establish the Jewish lineage for the Messiah (OT), and to Saul/Paul (as the resurrected Jesus in Acts 9:3-6), whom God chose to establish the NT church of Christ. Miracles are rare (not normative).