Renting for family, dogs and cat impossible?

Hi guys,
My family (2 kids + 2 small dogs + 1 cat), we've the project to move to Japan.

I heard from the beginning that renting a place is super hard in Japan, let alone in my situation + no stable job.

To be honest I can afford to buy a house of my need in Japan, and I thought this move would make things easier.
Things are, even with "good" budget, it's very hard to find a good house, near the school etc, lol. Not in term of price but simply putting like a lot of money to get something you don't even really like seems foolish.
I'm scanning for 12months, I see some house unsold for that long, always always the same.

But now that I'm really thinking about moving next year, I wonder if I didn't go too fast about rental and maybe there's a way.
I wonder if someone has my experience, and if there's anything doable? Maybe expat renting out to newcomers etc.

Any tips or experience welcome 🙂