K1 entrants can apply anytime before their I94 expires true, in their maiden name. K3 cannot apply at all until EAD approval. OP wants a SS card in married name - SS will require EAD in married name for OP to get what she wants. Getting a SS card in married name before EAD? Difficult to impossible. It it the number that is important anyway, gets you enrolled in health insurance, bank, credit card, life insurance, the whole puppet show.
Otherwise OP can get a SS in maiden name under K1 status and change her name on the card later after the EAD card is approved.
Recommendation to “convert to K3” is bogus and even if OP went home, started over, and managed to procure a K3 (miracle there) she would still not see a SS card until her EAD was approved.
