Happy to hear you like it ♡ And actually, it can be played in the order you want.
It's just that the Act 1 routes (Common, Lagi, Hiryuu) can be a good start since they give the first look at the whole background plot. But it's not necessary for you to fully enjoy the other routes.
But The Common Route is included in Act 2 as well, so if you want you can start with that :D