Well, the thing is, you can't just walk up to one and feed a beast and then tame it
The beast must take an interest to the player
It's something that happens on a rare occasion
And the tamable beasts in the game are limited in the first place, so there is a possibility that the first floor has none in the first place
I think it is most reasonable for the tamed pet to come into play later, rather than from the start

Anyway, I think it's good to go in the character page.
With the tamable beasts, I will check with Caits whether you can start with it or not. But, as I said, it's supposed to be rare, so it would be unlikely to occur so quickly.