As with Isabella on your other thread his birth is on the IGI (International Genealogical Index) on familysearch.org - this is free to search.
Andrew Vanbeck b.15/12/1863 Dalkeith, Midlothian, son of George Vanbeck and Mary Frazer (or Fraser). Siblings also baptised in Midlothian were:
Robert b.19/2/1868 Dalkeith
Elizabeth b.10/7/1872 Dalkeith
Mary b.24/11/1870 Dalkeith
George b.30/8/1873 Dalkeith
Donald b.16/5/1866 Liberton
1871 Census - Whites Close East, Dalkeith, Midlothian
Transcribed as 'Vanbrick'
George 33 Coal Miner b. Lapworth (?), Edinburghshire (Midlothian)
Mary 30 b. Liberton, ditto
Andrew 7 b. Dalkeith, ditto
Robert 3 ditto
Mary 4 mos ditto
I only have access to transcripts of the Scottish census but think 'Lapworth' is an error. You'd need to look at the original to see what that says.
Andrews' birth certificate shows parents as George Vanbeck and Mary Fraser and that they married 1/8/1862 at Liberton, Midlothian. Couldn't find the marriage so looked under Mary Fraser's name and found he'd married under the name Andrew (not George) Vanbeack, aged 21, Coal Miner - certificate states he was son of Andrew Vanbeack, Quarryman (deceased) and Elizabeth Vanbeack, formerly Clark. Mary Fraser 23 dau. of Donald Fraser, Ploughman and Mary Fraser, formerly Whitson.
Think his listing as Andrew could have been a mistake. He couldn't read/write so wouldn't have known.
1851 Census - Hammerman Land, West Wynd, Dalkeith, Midlothian
Isabella (?) Vanleck 35 Prin Winder b. Crown Head, Peebleshire
Jessie Vanleck 17 b. Inveas, Edinburgh
John Vanleck 15 ditto
George Vanleck 13 ditto
1841 Census - Bonnyrigg, Cockpen, Midlothian
Andrew Vanbeck 34 Shoemaker b. Scotland
Elizabeth Vanbeck 25 b. Scotland
Janet Vanbeck 6 b. Midlothian
John Vanbeck 5 ditto
Andrew Vanbeck 4 ditto
George Vanbeck 3 ditto
Think you are going to have fun with this surname - all sorts of permutations seem to be coming up. The 1841 Census only stated if people were born in that county or not - as Andrew and Elizabeth have Scotland given means that neither was born in Midlothian. The name Janet and Jessie are interchangeable in Scotland. Andrew Vanbeck senior appears to have died between 1841 and 1851 so have no idea where in Scotland he came from. It seems that the family were Catholic hence nothing in parish records on IGI. Scotlands People have some Catholic records but you have to buy credits I'm afraid.
Best I can do.
Annette
PS Just seen other replies but will post this as have some added information