In Exodus 3:12, this signifies a confirmation of the truth that the Divine proceeded from Himself. (Arcana Coelestia 6870)

(References: Arcana Coelestia 1039, Genesis 9:12, 9:13, 9:17)

18. 'The face ¹ of the deep' is that person's desires and resulting falsities, of which he consists and in which he is completely absorbed; and because he has no light at all he is like the deep, or something thoroughly obscure. Throughout the Word such people are also called 'the deep' and 'the depths of the sea' which are dried up or laid waste until a person's regeneration starts, as in Isaiah,

Awake as in the days of antiquity, the generations of long ago. Was it not You that did dry up the sea, the waters of the great deep; making the depths of the sea a road for the redeemed to go across? Let the ransomed of Jehovah return. Isaiah 51:9-11.

Furthermore, when looked at from heaven, this kind of person resembles a darkened mass with no life to it. The same expressions embody within them in general the vastation in man, described many times by the Prophets, which precedes regeneration. For before a person can know what truth is, or be moved by good, the things that hinder and offer resistance must be removed. Thus the old man must die before the new one can be conceived.

Footnotes:

6870. 'And this will be the sign to you that I have sent you' means the recognition that the Divine would go forth from Him. This is clear from the meaning of 'the sign' as the corroboration of truth and consequent recognition that it is indeed so; and from the meaning of 'being sent' as going forth, dealt with in 2397, 4710, 6831, so that 'being sent by God' is going forth from the Divine. It is also the Divine going forth from Him, for one who comes forth from the Divine is receptive of the Divine and extends its influence further.