The argument of Spinoza's Ethics is:
Prop.XI. God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists.
Proof. If this be denied, conceive, if possible, that God does not exist: then his essence does not involve existence. But this (Prop.VII) is absurd. Therefore God necessarily exists.
The "essence implies existence" relies on:
Prop.VII. Existence belongs to the nature of substances.
Proof. Substance cannot be produced by anything external (Corollary, Prop.VI), it must, therefore, be its own cause—that is, its essence necessarily involves existence, or existence belongs to its nature.
and this, in turn, with the definition of God:
Def.VI. By God, I mean a being absolutely infinite — that is, a substance consisting in infinite attributes, of which each expresses eternal and infinite essentiality.
licenses the conclusion.
Comment
Seemingly, in the "proof" of Prop.IX we need also:
Ax.VII. If a thing can be conceived as non-existing, its essence does not involve existence.
Thus: "conceive, if possible, that God does not exist [...] But this is absurd. Therefore God necessarily exists."
In conclusion, we can state at least two "debatable" points:
is it really "absurd" to conceive "that God does not exist" ?
is it really necessary that for substance "essence involves existence" ?
