No. The spiritually dead - and everyone is spiritually dead before becoming saved/born again- cannot believe the truth. True belief accompanies spiritual life not spiritual death, but life is only given by God, not by man. Observe in the verses following, those in them played no part whatsoever in the receiving of spiritual life: they were dead in sin, but God, by His grace and mercy alone, gave them spiritual life, period. They contributed nothing whatsoever to it - solely being recipients. The spiritually dead, being spiritually dead - just as physically dead are physically dead- cannot give anything to themselves - therefore, the dead are completely at God's mercy for life, utterly unable to give it to themselves. And as dead, neither can they give to themselves true faith nor belief.
But He does give them freely to those chosen from before the foundation of the world.
[Eph 2:1 KJV] 1 And you[hath he quickened], who were dead in trespasses and sins;
[Eph 2:5 KJV] 5 Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved;
[Col 2:13 KJV] 13 And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with[G4862] him, having forgiven you all trespasses
