Your question has already been answered by @Chocolate above, so all I am doing would be to add my own perspective.
The second line would mean:
"A/The mythology of the universe starts again today."
It is "today too" and not "mythology too" because 「も」 generally modifies the immediately preceding word.
Why use "today" at all in the first place? IMHO, that would be because this is a theme for anime, correct? In a televised anime series, the viewers would naturally tend to expect an interesting story to take place in each episode. By saying 「宇宙の神話 今日もはじまる」, it inspires a feeling of hope that something exciting would happen again today in the episode that one is about to watch.
In that sense, one could say that the lyrics for anime themes can be subtly "commercially manipulated" like this. In other words, anime theme lyrics should not be analyzed too straightforwardly using the regular prose/composition grammar or phrasing.