Usually with rescue dogs it's complete guesswork as to how old they might be. 'Gotcha Days' replace birthdays to mark the dog's adoption date, and how long dog and owner have been together.
We rehomed Beau privately from a local family who had had him since a pup so his birthday and age was known, and although he does have a 'Gotcha Day' (29th September 2009), I choose to mark his birthday instead. And by chance, me and Tilly did meet him as a pup when co-hosting a puppy party at our local vets ~ not that I suppose he remembers this!
So Happy 3rd Birthday beautiful Beau ... enjoy your cake!