I have his marriage certificate which is dated 1904 and he was aged 28. I also have a death notice where he died in a works accident in 1925 aged 53, so born 1875/1876. On his marriage certificate his is shown in the army in Clarence barracks Portsmouth. His father is recorded as Simeon Adams (deceased) Butcher Journeyman.
As this is an old post, I don't know if you're any further forward with Stanley by now.
There is a Stanley Adams on 1901 census, a gunner in RGA, single, stationed in Jersey, born in Bristol abt 1875. Could he be your man?
FindMyPast has military record of this Samuel.
He attested on 24 Oct 1895 at age of 20 yrs and 2 months. His birthplace given as parish of St Phillips Bristol. He was discharged on 23 Oct 1907, re-enlisted 2 Sept 1914
Next of kin: mother - Mary Adams, 1 Windsor Grove, Upper Easton, Bristol.
This information puts his birthday abt Aug 1875, so registered Q3, possibly Q4 if the parents waited until the last opportunity. It looks like his army enlistment was for a 12 year term and he joined up again when WW1 broke out.
I haven't found any Samuel Adams births registered in Bristol at the right time, but several Samuels so he may well have changed his name. When people change names they frequently keep the same christian name so it may be worth trying to track the Samuels born in Q3/4 1875.
Also there appears to be no sign of Samuel the soldier before 1901 at least not under the name Adams and he should be on the 1881 and 1891 censuses. No sign of Mary or Simeon Adams either. The fact his mother is next of kin implies his father had died by 1895 when he joined army.