I know what you mean Cedas, as I have spent over 17 years looking for the birth records of my G Grandfather John Williams, with no luck. I have even visited Wales twice looking at the records at the records offices, but with so may Wiliams, it ws mid boggling to say the least

Here is what I have so far and as you can see, with no birth father, and no maiden name for his mother, it's a lost cause
1851 Census for Greenfeild, Holywell he was aged 26...birth year 1825
1855 He emigrated to Oz aged 28 aboard the Marco Polo, together with an Evan Williams aged 28 also...........................Johns birth year now 1827
1858 He married Elizabeth Liddell @ Northdown,Tas...aged 30...now b/yr 1828
1913 He died aged 89..................so now birth year 1824
So maybe you can see why I can't find him
On the 1851 census, when he was working for James SIMON at Greenfield, Holywell, and living at Tai Coed 13 with his widowed mother Anne aged 65 & a pauper, her place of birth listed as Penlan, Anglesey, while Johns was given as Ceirchiog, Anglesey.
On the census the Simon Family of Greenfield Farm, was listed as no 197 while Tai Coed 13 was listed as no 192
I also found an Owen Williams aged 38 born Ceirchiog, living at 122 Ravenyard. Could this be his brother?
I am assuming his father was named Richard from the naming of his children (listed below)with wife Elizabeth.
1...Anne (his mothers name
2..Richard
3.. Hugh....(his father-in-law)
4..John...( himself)
5...Elizabeth..(his wife)
6..William
7..Alice Louisi
8.. Jane May
9..Email Agnes.. ( Agnes from Liddell side)
10..Andrew Owen.
Cheers, Tassie