NKJV

^{1 Tim 2: 12} And I do not permit a woman to teach or to have authority over a man, but to be in silence. ¹³ For Adam was formed first, then Eve. ¹⁴ And Adam was not deceived, but the woman being deceived, fell into transgression. ¹⁵ Nevertheless she will be saved in childbearing if they continue in faith, love, and holiness, with self-control.

Although it was Eve who sinned first but Adam being the “federal headship/covenant headship” the consequence of his fall resulted in the imputation of his guilt to all humanity.

“She will be saved in child bearing” – meaning, she alone will be saved through her child bearing.

Romans 5 : ¹² Therefore, just as through one man sin entered the world, and death through sin, and thus death spread to all men, because all sinned—

^{Romans  5:14} Nevertheless death reigned from Adam to Moses, even over those who had not sinned according to the likeness of the transgression of Adam, who is a type of Him who was to come.

^{Romans 5:19} For as by one man’s disobedience many were made sinners, so also by one Man’s obedience many will be made righteous.

Timeline  :  Sin and salvation according to Paul in his discourse on Romans 5,

SIN  {     Eve ..    [ salvation  ( Adam – – – – – – end of humanity ) ]     }

 Eve who transgressed before Adam, fall outside of Rom 5: 12, 14 , 19. But she (EVE) will be saved in bearing the first daughter and then from that daughter through the maternal line to Mary/mother of Jesus. Therefore, all the offspring of Adam including the women (they) leading to birth of Jesus, fall within the salvation plan delineated by Paul, (if they continue in faith, love, and holiness, with self-control).