A very interesting question, which looks like it was asked by a native speaker, got migrated to English Language learners:
The question asks whether the word ever is modifying the verb be or the word first in the sentence:
- It was my first game ever.
It is difficult to tell why this grammar question got moved to ELL. In any case, at least one of the migrates said in a comment that ever was a modifier in the verb phrase was my first game ever. However, the OP would be right to find such a claim problematic because we cannot say:
- It was ever my first game
Or, rather, we can, but the meaning is completely different. Compare that with.
- I wasn't sad ever.
- I wasn't ever sad.
Here we can move the ever around from end to mid position.
There are numerous other interesting quirks and problems here.
Just because the sentence is short and easy to understand does not mean the grammar is simple. This is a question worthy of the interest of linguists and serious language enthusiasts. Please can we get it back before it slips down the questions list and loses all its momentum.