Looking for them on the 1911 census, I can only see one Sydney and Ethel Smith who have been married under a year and that is a couple living at 19 Protheroe Street, Fernlea, Glamorgan in South Wales a long way from London or Woolwich which makes it rather doubtful that they are your couple. However this Sydney Smith (no other names or initials given was age 29 which seems correct and he gives Dartford Kent as place of birth which show there is a connection close to Woolwich. Edith is age 25 and gives Alverstoke Hants. as PoB, as you presumably have information on her, then if she fits there is a good chance that they may be correct.
I cannot see any births in Dartford around the early 1880s for either a Sydney (or Sidney) George or Daniel Smith, however there are some registered just Sydney (or Sidney) in Dartford or nearby. Second or further names are often added at baptism or later so any could be the one that you are looking for, there is one Sidney George Smith in the West Ashford district in Dec. 1882,but that is many miles from Dartford. There are also a number of possibles on the 1891 and 1901 census.
I suggest that you purchase a copy of the marriage certificate which should give Sydney's father's name and occupation, providing he knew his father, which may assist in spotting him on an earlier census, enabling you to narrow the search.
Sydney Smith in the 1891 England Census
Name: Sydney Smith [Sidney Smith]
Gender: Male
Age: 8
Relationship: Son
Birth Year: 1883 [1882]
Father: Henry Smith
Mother: Elizabeth Smith
Birth Place: Chesterton, Cambridgeshire, England
Civil Parish: St Andrews
Residence Place: Chesterton, St Andrews, Cambridgeshire, England
Sub registration district: Fulbourn
ED, Institution or Vessel: 1
Neighbors:
Piece: 1280
Folio: 8
Household Members:
Name Age
Henry Smith 46
Elizabeth Smith 42
William Smith 19
George Smith 16
Sydney Smith 8
Ethel Smith 6
Lilley Smith 4
Alice Smith 11/12
ALSO FOUND
Sydney Smith in the Birmingham, England, Church of England Baptisms, 1813-1912
Name: Sydney Smith
Age: 1
Birth Date: 30 Apr 1882
Baptism Date: 25 Jun 1883
Baptism Place: Aston Brook, St Mary, Warwickshire, England
Parish as it Appears: Aston Brook, St Mary
Search Photos: Search for 'Aston Brook, St Mary' in the UK City, Town and Village Photos collection
Father: George Smith
Mother: Eliza Smith
ALSO FOUND
Sydney George Smith in the 1891 England Census
Name: Sydney George Smith
Gender: Male
Age: 8
Relationship: Son
Birth Year: 1883
Father: David Smith
Mother: Harriett Louisa Smith
Birth Place: Derbyshire, England
Civil Parish: Litchurch
Residence Place: Derby, Litchurch, Derbyshire, England
Sub registration district: Derby
ED, Institution or Vessel: 56
Neighbors:
Piece: 2735
Folio: 28
Household Members:
Name Age
David Smith 36
Harriett Louisa Smith 37
Henry Smith 13
David Smith 10
Sydney George Smith 8
Miranda Smith 6
George Smith 4
Edgar Smith