As @Kai has mentioned, it is ambiguous and you'll have to make your own judgement call. I've written down a good chunk of information that may convince you either way.
Disclaimer: I believe it is blitzball which came first, but I have tried to make this balanced
- 1000 Years Ago: Machina War, Destroyal of Old Zanarkand
- End of Machina War: Creation of Dream Zanarkand, Sin
- In-game Present Day: Tidus leaves his home, Dream Zanarkand
When the Machina war neared the end, it was clear that it was being dominated by Bevelle thanks to the help of their machina Vegnagun. Yu Yevon was on the side of Zanarkand (Anti-Machina) who were slowly being destroyed.
In order to preserve the city, Yu Yevon turned the remaining citizens of old Zanarkand into the Fayth. The Fayth then created Dream Zanarkand, based off of memories of their life in the old city. To protect this place of peace, Yu Yevon created Sin to defend Dream Zanarkand and rid the world of traces of machina. Yu Yevon may not have been a symbol of religion at this stage, but he had a large following. It would not be strange for a community of a united cause to have a symbol of respect and unity while he lived.
The dream Zanarkand is composed merely of the Fayths memories of the old city and their lives. It also resides in a space distinct from the rest of the world. These two facts combined give us evidence that the Fayth must have known of the symbol before Dream Zanarkand was constructed.
The point of Dream Zanarkand was to restore Old Zanarkand to it's pre-war state and to preserve it for eternity. Since Dream Zanarkand was pre-war - there would have been no large following of Yu Yevon as the powerful summoner defence against the machina. Even if this symbol was in use, it is much less likely that an already established sport would take on the idealisms and symbolisms of one man's following, than it is to believe that Yu Yevon adopted the symbols as they were already representative of victory and strength.
In the first moments of Final Fantasy X, we follow Tidus in Dream Zanarkand, many traditions have been forgotten as years have gone by. Souls no longer need to be sent, there is no evidence of the existance of aeons, and the Hymn of the Fayth no longer holds any meaning. This is the main point of contention - Does the fact that the Hymn exists mean that the Hymn originate from the fayths' subconsciousnesses as they reside in the world (Not related to Yevon)? or was the dream city created to represent the city whilst Yu Yevons still had its following (Originates from Yevon, Possibility the symbol does also)?
The Hymn of the Faith roughly translates to (after some puzzle solving seen in the link):
Pray to Yu Yevon
Forever and ever
Grant us prosperity
The lyrics indicate the acknowledgement of the Fayth's creation by Yu Yevon and how they are to reside there forever and ever in a dreamlike peace. This makes the song even more important in assessing the timeline of the symbol.
The wikia and other sites claim that blitzball came first, but none cite any solid articles or go into more detail than passing mentions. Therefore, you must decide yourself which possiblity you believe is more plausible.