Of interest - There is a birth notice on 1 May 1920 for a child of H TAYLOR and Annie (nee NAISBIT) of the same address as above - 173 Sturt St.
https://trove.nla.gov.au/newspaper/article/37515343 (1st column, bottom)
Harold TAYLOR married Annie May NAISBIT in 1919 registered at Norwood (279/313). A possibility - there is a birth for a Harold TAYLOR son of Thomas TAYLOR in 1895 in Adelaide (570/320). A brother /half brother of Hilda May?
His army record (attestation Dec 1914) has the same address as Francis Harmer SMITH - Frederick Place off Sturt St. Father is Thomas TAYLOR
https://recordsearch.naa.gov.au/SearchNRetrieve/Gallery151/dist/JGalleryViewer.aspx?B=1930201&S=1&N=90&R=0#/SearchNRetrieve/NAAMedia/ShowImage.aspx?B=1930201&T=P&S=1
(note on page 10 in red says mother is Margaret TAYLOR)
Birth registration for Harold TAYLOR born 1895:
urname: TAYLOR
Given Names: Harold
Date of Birth: 30-Aug-1895
Gender: M
Father: Thomas TAYLOR
Mother: Maggie STOKES
Birth Residence: Adelaide
District: Adelaide
Book/Page: 570/320
Marriage registered for Thomas TAYLOR and Maggie STOKES :
Groom Surname: TAYLOR
Groom Given Names: Thomas
Bride Surname: STOKES
Bride Given Names: Maggie
Marriage Date: 25-Jun-1889
Marriage Place: Res of Rev E G Day Adelaide
Groom Age: 28
Groom Marital Status: S
Groom Father: George TAYLOR
Bride Age: 24
Bride Marital Status: S
Bride Father: Patrick STOKES
District: Adelaide
Book/Page: 159/854
Given that all of Hilda May's BDM registrations found in GenealogySA show her maiden name as WELCH, it looks as if she was conceived out of wedlock.