Which came first, LEGO or Pakistan?

LEGO came first, by 15 years. Ole Kirk Christiansen started making wooden toys in Billund.

Side by side

LEGO

The company began in 1932 making wooden toys; the name comes from leg godt, Danish for "play well". The interlocking plastic brick in its modern form was patented on 28 January 1958, and the tolerances have been held so precisely since that a brick made that day still clutches a brick made today. LEGO is now the largest tyre manufacturer in the world by unit count.

Pakistan

Pakistan and India were created by the same act of parliament, but Mountbatten had to attend both ceremonies, so he took the Pakistani one in Karachi on 14 August and the Indian one in Delhi on the 15th. Pakistan is therefore one day older than India in the sense the question means. Independence in both cases took effect at the same instant: midnight between the two dates.