Om Sairam.
If Sai wished to have shared the date of inception of his avatar in human form he would have sure shared it. He didn't share it because he wanted to symbolize there's no beginning or end to him.
This day, date, and time are concepts started with Sunrise and Sunset. There was no real time before Sun and Moon was created by God. There was only being or existence and it is called beginningless beginning. So there can never be a birthday for Sai
And it’s better not to limit him with attributes of a person of 3.5 cubits length like said in SSC.