Published family genealogy states that her eldest child was likely born ca. 1657.
According to reasonably reliable sources the marriage date of 1650 is correct, and she was born ca. 1632 (shortly after her parents landed in New Amsterdam, which was in 1631). 1632 would clear up the inconsistency regarding her youthfulness at time of marriage (now showing age 15).
I could correct the birth date, but the name fields are locked.
Sources state that her maiden name was Jansen (Americanized spelling from the original Dutch variation).
Her father (whose father was Dutch) was Anthony Jansen van Haarlem who became the Admiral of the Sultan of Morocco’s fleet at Salee (Salé, Morocco). van Haarlem simply indicates where he was born or raised.
von Salee is not their surname. Geni has her father's surname correct, but somehow got his children's wrong. I don't understand why Wikipedia ignores his official surname in favor of his alias, but he didn't use that alias himself in official records other than possibly to distinguish himself from all other "Anthony Jansens" when conducting business. Wikipedia does make it clear in footnotes that "von Salee" is just a variation of his real name. I think von Salee belongs in the "also known as" field. It's a nickname, not his real name.
Anthony's father was also born Jansen: "Jan JANSZOON van Haarlem, commonly known as Reis Mourad the Younger, was a former Dutch pirate who became a Barbary corsair in Ottoman Algeria and the Republic of Salé. After being captured by Algerian corsairs off Lanzarote in 1618, he converted to Islam and changed his name to Mourad."
It was common in those times for Christians captured by Muslim pirates to convert to Islam or face serious consequences. After falling under captivity and marrying a Muslim woman, their son Anthony grew up in that world of piracy, eventually becoming the Moroccan sultan's admiral.
But plainly he left that life at some point, returned to Holland and married the widow five years his senior who would sail with him to New Netherlands and start a family of four daughters.
I'm a little surprised to find their name fields locked in with the wrong information. To their American descendants, they are the Jansens.
https://www.geni.com/documents/view?doc_id=6000000198221738826
https://www.geni.com/documents/view?doc_id=6000000198221738828
https://en.wikipedia.org/wiki/Anthony_Janszoon_van_Salee#cite_note-1
https://longislandgenealogy.com/Surname_Pages/southard.htm#:~:text=....
https://www.wikitree.com/wiki/Southard-61#_note-4
https://archive.org/details/Biographies-06/3660%2002%2003%20Jansen%...
Also it appears that her husband was born in England (not Leyden, Holland). Looks like the two Thomas's, although related (cousins? x?) got mixed up here. The Dutch one is actually "Southworth".
https://www.wikitree.com/wiki/Southworth-112
https://www.wikitree.com/wiki/Southard-61
(Note that WikiTree also has Annica's maiden name / surname wrong).
https://www.wikitree.com/wiki/Jansen-455
WikiTree does however include the original manuscript marriage license for Annica's parents: Anthonis Janss ("Jansen" abbreviated) and Grietje Reijniers.
Grietje, a barmaid, had been married in Amsterdam about three years earlier, on 26 Sept 1626, to a tailor named Albert Egberts. In the record of this marriage her age appears as 24, so she would have been born in 1602 and was 5 years older than Anthony. Her first husband d. in 1628 and there were apparently no children.