Chinlo - hard to say, because I think that the use of both names as first names has only become widespread since the late 20th cent.
Regarding the age of the words themselves:
Finlay seems originally to have been a descriptive surname - it appears in written records from the 1400s, but very few systematic surname records survive in Scotland from before that time. The patterns of naming were different from today, as well. The Gaelic words 'fair' and 'warrior' are much, much older, of course.
Finn is best known as a descriptive nickname, eg for the Irish mythical hero, Finn MacCool. (His 'real' first name was something else.) Many legendary early Irish kings had the same nickname. All their stories were first written down by Christian monks between the late 11th-15th centuries. They are hundreds of years older, although it's very hard to tell how far the monks shaped and changed the traditional tales.
One legendary early Irish king was listed as 'Finn Mac Blatha'. Traditionally he lived in the first millenium BC. So perhaps it's possible to count that as the first use of the name? I don't know.
In more recent times, Finn has sometimes also been used as a short form of Gaelic names such as Fintan and Finbar. These are old names, too, and were recorded very early; there was a St Fintan who lived around AD 650, for example, and a famous Bishop Finbar who lived around AD 550.
Innthenick - I honestly think there's a regional spectrum, from 'Fyonn' and 'Fiown' to 'Finn' and even 'Feen'. This is illustrated by these examples, all by native Irish speakers: forvo.com/search/Fionn/ It's a self-selected sample, of course...Probably I should have said 'sometimes pronounced 'Finn''.