I cannot manage better than 3 turns, I think this might be a hard limit for the current set of options.
T1: Borrow, Baker coin; Inherit(Dc)
T2: E (trash E): $5, Borrow: Tfair, Mission, Alms (gain Prssn)
T2M: Prssn -> E (trash E, trash E, gain nothing): $10: buy Tfair x2, Exp x2, Alms (Csmith)
//draw everything
T3: Prssn -> Csmith (trash Csmith, gain Bom): $21: Tfair x2, Kc, Mission, Mint(trash 7C)
T3M: PrssnBomKcMint: Kc -> Bom (Dc: trash Prssn, Mint): Bonfire (trash KcBom)
A similar option
T1: Borrow, Baker coin; Inherit(Dc)
T2: E (trash E): $5, Borrow: Tfair, Mission, Alms (gain Wv)
T2M: Wv -> E (trash self) -> E (trash self): $11: Summon (Prssn), Exp, Alms(Csmith)
T3: 6CWv: [Prssn] -> Wv (draw CsmithC, trash Wv, gain Bom) -> Csmith: $14: Mission, Mint, Bom
T3M: Prssn -> Bom (Dc:trash Mint, trash, Csmith, trash Bom, gain nothing): Bonfire (trash Prssn)