This is seen at the beginning of Paul’s epistles and it is Paul’s way of saluting the readers of his letters. Trying to use only the direct meaning of those words to determine the intentions of Paul might be misleading because though grace and peace are words with their own natural meaning, they were used in this case by Paul for a different purpose which is to salute his readers, although with a prayerful undertone. It must have been a common expression in those days because Peter, John and Jude also used it to salute the readers of their letters. (2 John 1:3, Jude 1:2, 2 Peter 1:2, 1 Peter 1:2). Just the way we would use “God bless you” in our contemporary world, it is used for salutation or to express gratitude, the same way “halleluyah” is used to request decorum. Someone who is not familiar with the way we use those expressions today will definitely miss our intention. Similarly grace and peace here is a greeting but then with a prayerful tinge. If we are to consider the role it plays in that letter it definitely is a salutation.
Notice, Paul didn’t greet them directly in Ephesians 1:2 but said the greeting is from God and Jesus. He said that as a messenger, pointing the readers of his letter to the fact that he was sent by God; hence he brought greetings from the one that sent him. I also noticed other authors that I mentioned above did the same thing. It really must have been a common way of saluting their readers. More than the salutation I discussed above, it also reveals the prayerful undertone I said it carries. Still with the example I used earlier, someone might greet a fellow and the person responds by saying “God bless you”, he definitely could have just said “bless you”, and in fact some people say that. But people usually like to add God because, although they said that purposely to respond to greeting or to show gratitude to such kindness but their response has a prayerful undertone of saying God should in the real sense bless that fellow. I think Paul used “grace and peace from God” in this manner.