Although I can't find a birth, the New South Wales police gazette and the Sydney Wilson you have in 1900 are not the same person.
Glebe. warrant issued by the children's court bench for the arrest of Sydney Ernest Wilson charged with disobeying a magisterial order for the support of his wife and children. aged 47, 5 feet 11 inches tall, stout build, fair complexion and hair, eyes blue, clean shaved. usually dressed in grey suit and grey felt hat drives a Buick car no. 39962 for private hire. is supposed to have gone to country.
published 28th july 1926
It does seem to match Wilson Sydney also record has been transcribed wrong. Wife is May not Mary. the second attestation form for Sydney also matches warrant.
Hope this helps in some way.