Alice is currently linked to Elias Stileman, Sr. as her father but this can't be true because that would mean she was born 9 years before her parents were born. Also, she doesn't show up on the Winthrop Fleet Passenger List with the rest of the family when they sailed from England to Salem in 1630. The only Stilemans listed were Elias, wife Judith and their son Elias Jr.
https://familypedia.wikia.org/wiki/Winthrop_Fleet_Passenger_List
The Stillman family history says her father was Robert and that she was niece of ELIAS STILEMAN, and sister of Richard Stileman, both of Salem [Waters 112]. She married Samuel Sharp in 1629 in England and had a daughter Abigail there shortly after.
http://www.stillman.org/sharpe.htm
Here's a Stileman family tree that I found.
https://archive.org/stream/pedigreesfromvis64beno#page/38/mode/2up
I just created a profile for Robert Stileman and moved alice so now she's his daughter. I also created a profile for his son Robert.
Oops. In my first comment I meant to say that Alice was born 9 years before Elias and Judith were married (not born).
I found a church register showing that his brother lost 3 children at once from the plague in 1609. Looking through the register, I found several others in other years who also died of plague even though it wasn't a year where there was a huge epidemic going on. Maybe that's what happened to Elias's missing children.