I want to expand a little more on this.
5 star tera raids (including event 5 star raids) will start appearing immediately after you beat the "The Way Home" storyline and the credits roll. This means that unless you beat the main story, you won't be able to access your own game's event tera raids.
However, you can still join tera raids hosted by another person's game via online or local communication, allowing you to access event raids.
If joining another person's raids isn't an option, you can always connect to the Poké Portal News to receive the event raids and outbreaks, and as long as you don't connect to the Internet after the event raids end, they will remain in your game indefinitely until you connect to the Internet again. In your case, this is the best option for you if you are absolutely unable to finish the game at the current moment, since you can beat the game and catch Rayquaza at a later date.
Do note that you don't need an online membership to connect to the Internet to receive the Poké Portal News, but you do need to link a Nintendo Account (this is for those reading who may not have known this).
Hope this helped and you are able to get your Rayquaza soon!
