TGA[] can be used as input for \gamma^0 in 4 dimensions and is transformed into DiracGamma[ExplicitLorentzIndex[0]] by FeynCalcInternal.
Overview, GA, DiracGamma.
TGA[]\bar{\gamma }^0
TGA[] // FCI // StandardForm
(*DiracGamma[ExplicitLorentzIndex[0]]*)TGA[] . TGA[] // DiracSimplify1