In the main comics continuity Natasha was born c. 1928. The basic outline of Natasha’s origins are explained in my FAQ, and that page also has links to my more in-depth Secret Origins series of essays. (These probably could stand to be updated, but should still be pretty informative.)
It’s misleading to think Natasha has a “serum like Steve” and I’ve gone into why. I’ve also previously explained the meta-history of Natasha’s agelessness, which is more complicated than popularly imagined. (It’s neither a recent invention nor a particularly consistent part of her character.) I’ve also posted some thoughts specifically on the importance of WWII to her canon.