Hi Neal,
Welcome to Talking Scot

Like Mary, I assume you have found the submitted IGI entry and are trying to prove it:
James Burdick
Birth 7 Mar 1744, Scotland
Spouse: Phebe Smith
Marr: about 1766 Sussex, New Jersey
I have gone out a bit farther on a phonetic limb than Mary

and searched for James b*r*k, leaving out the /d/ in case it came up as a /t/ or /th/, all possible variants. On Scotland's People (link at the top of this page) there are 19 James b*r*k born in Scotland between 1740 and 1750. None of them is spelled Burdick, nor even Burtick, but there are some plausible variants, I think:
29/03/1740
BARRACK JAMES
JOHN BARRACK/
Methlick /ABERDEEN
01/05/1748
BARRACK JAMES
JAMES BARRACK/MARJORY TAYLOR
New Deer/ABERDEEN
11/05/1746
BERRICK JAMES
JAMES BERRICK/MARGARET CHAPMAN
Markinch/FIFE
09/02/1744
BERWICK JAMES
JAMES BERWICK ELSPETH HORN
St Andrews and St Leonards/FIFE
28/08/1748
BERWICK JAMES
WILLIAM BERWICK MARGARET RUSSELL
St Andrews and St Leonards /FIFE
10/08/1746
BORTHICK JAMES
THOMAS BORTHICK/
Jedburgh/ROXBURGH
30/05/1745
BORTHWICK JAMES
JAMES BORTHWICK/MARGARET RICHARDSON
St Cuthbert's EDINBURGH CITY/MIDLOTHIAN
31/07/1748
BORTHWICK JAMES
GEORGE BORTHWICK/AGNES CHALMERS
Edinburgh EDINBURGH CITY/MIDLOTHIAN
24/01/1748
BORTHWICK JAMES
ALLEXANDER BORTHWICK/ISOBEL PAISLEY
Langholm or Staplegorton /DUMFRIES
30/03/1749
BORTHWICK JAMES
GEORGE BORTHWICK/JANET PORTEOS
Moffat /DUMFRIES
None exactly matches the date of birth in the submitted entry

And even if you were to look at all the christening records, it is impossible to tell from them which one of these wee lads might have hopped on a ship for New Jersey

I'm afraid that more research will need to be done on the American side of the Atlantic, to try to ascertain where he came from and/or the real date of his birth.
I really sympathize, since I have at least 3 Scottish lines that are stuck on the east coast of the U.S. and no way to make the jump back to Scotland

Is there anything else at all you can tell us about this man?
All the best,
Sarah