If this is an English/Welsh birth registration you can look at the index quite quickley to establish possibilities. Firstly if you know the area/town the family lived in that will help greatly, because the registration distict is given in the index. If you do not know the child's first name, then look at the index for the suname and district to create a list of possibles. What would actually be quicker though is to go thru the death index and look for a child aged approx 2 yrs old, (as ages are given in the index) registered with the correct surname in the possible district that looks right, then jump back to the approx bith year for the registration of that child to see where the birth was registered. (the index is available on ancestry.co.uk) Each year is divided into 4 quarters, Q1 jan -mar. Q2 apr - jun Q3 jul - sept Q4 oct - dec. Once you have done these searches you can obtain copy certificates from the local register office that holds the original registers now.