Ummm

I think the surname was BUDGE in the 1840s ....
From the historic records section of the website
https://beta.familysearch.org/ William Bridge, born 11 May 1843, baptised 26 Nov 1843, at Hunter’s Hill, parents Daniel and Matilda
Mary Ann Budge born 25 June 1845, baptised 28 Sept 1845 at Hunter’s Hill, parents Daniel and Matilda
James Burge born 26 Jan 1848, baptised 16 Jul 1848 at Parramatta, parents Daniel and Matilda
George Thomas Burge born 11 Oct 1855, baptised 4 Nov 1855 at Parramatta, parents Daniel and Elizabeth Matilda
From NSW BDM online index
1843 William Budge, Vol 27A, line 3789, son of Daniel and Matilda
1845, Mary A Budge, Vol 30A, line 1174, dau of Daniel and Matilda
1848, James Burge, Vol 33A, line 8973, son of Daniel and Matilda
1855 George T Barge, Vol 42B, line 3469, son of Daniel and Elizabeth M
It would be interesting to see what the details are for that Vol 27A and the 1843 entries ….. Line 3789 should be for William BUDGE and line 3799 should be for William BRIDGE…. And both sets of parents recorded as Daniel and Matilda…...
Cheers, JM