Ein Sof's insistence that nothing whatever can be predicated of God did not appear from nowhere; it stands in a long tradition of negative, or apophatic, theology that the kabbalists inherited and then pushed in a distinctive direction.
Maimonides, writing a century or so before Ein Sof became standard kabbalistic vocabulary, argued in the Guide of the Perplexed that every positive attribute predicated of God, wise, powerful, existent, is either a statement about God's actions in the world or a denial of the corresponding defect, so that to say God is "living" really means only that God is not to be classed among the dead or the inanimate. Maimonides drew heavily on the Islamic philosophical tradition, particularly on Al-Farabi and Avicenna, which had itself inherited the negative theology of late antique Neoplatonism, chiefly the idea, traceable to Plotinus, of a supreme One beyond being, beyond thought and beyond every category, from which all multiplicity proceeds by emanation.
The kabbalists took over the destination, an ultimately unknowable divine reality, but rejected the philosophers' account of how anything follows from it. Where Maimonides treated the philosophical inquiry into the divine attributes as the highest exercise of created reason, and Neoplatonism described emanation as an impersonal, necessary overflow, Kabbalah retained the strict apophaticism concerning Ein Sof while insisting that the process by which the sefirot emerge is nonetheless personal and addressed by scripture and prayer, one reason some kabbalists were suspicious of philosophy even while borrowing its vocabulary.