The phrase 'the same goal' is correct and usable in written English. It can be used when referring to two or more people or things that all have the same objective. For example, "My brother, cousin and I all have the same goal of becoming successful business owners."
I have the same goal".
"We all have the same goal.
For the same objective, the same goal.
But we had the same goal.
"This is the same goal as Ithkuil.
"I think we have the same goal.
But both seek the same goal.
We have the same goal".
But it's basically the same goal".
All of us have the same goal.
So we have the same goal.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union