Walter Kaiser on Genesis 3:15 and 4:1 -- Eve's expectation of her first born.

Walter Kaiser Jr. traces the path of the Promise through both the Old Testament and the New Testament. He makes some observations about Genesis 3:15 and 4:1.

But in the midst of the dirge of gloom and rebuke came God's surprising word of prophetic hope (Ge 3:15). A divinely instigated hostility--"I will put enmity between you [the serpent] and the woman, and between your offspring [or seed] and hers--is climaxed with the triumphant appearance of a "he"-- no doubt a representative person of the woman's seed. He would deliver a lethal blow to the head of Satan, while the best the serpent would be able or even permitted to do would be to nip the heel of this male descendant.

Who this male descendant was, was not immediately revealed. Perhaps Eve thought Cain was the one. She named her son Cain (Heb., qayin), saying she had "gotten (Heb.,qaniti) a man, even the Lord" (4:1); at least, that is a fair way of rendering the enigmatic phrase. Regardless of whether one agrees with this rendering, she was mistaken, and the biblical text only records her longings and perhaps gives us an insight into how an clear an understanding she had of Genesis 3:15 -- she expected that God would supply a person who would care for their sin that had occasioned the fall. (The Promise Plan of God by Walter Kaiser Jr., p. 43)

There is a footnote by Kaiser that Luther interpreted the passage this way in the German bible.

Other references that indicate that Old Testament believers were looking forward to the Promised Seed:

To Seth also a son was born, and he called his name Enosh. At that time people began to call upon the name of the Lord. (Genesis 4:26, ESV)

When Lamech had lived 182 years, he fathered a son and called his name Noah, saying, “Out of the ground that the Lord has cursed, this one shall bring us relief from our work and from the painful toil of our hands.” (Genesis 5:28-29, ESV)

When Abraham puts his faith in God's promise that Abraham's seed will be from his own body, then that belief was counted as righteousness.

And behold, the word of the Lord came to him: “This man shall not be your heir; your very own son shall be your heir.” And he brought him outside and said, “Look toward heaven, and number the stars, if you are able to number them.” Then he said to him, “So shall your offspring be.” And he believed the Lord, and he counted it to him as righteousness. (Genesis 15:4-6)

Israel prophesies that from Judah the kingly line will come in Genesis 49:10.

The scepter shall not depart from Judah, nor the ruler's staff from between his feet, until tribute comes to him; and to him shall be the obedience of the peoples. (Genesis 49:10, ESV)