Just was thinking over things today, and how hard it can be to start off with just two wolves. So my suggestion is fairly simple: Maybe new accounts can get a free token that lets them automatically catch a wild wolf. To keep it from being too easy and therefore encouraging people to try to make dozens of accounts, maybe they only get the token after they've completed a few quests. Maybe like, 3-5? Or enough that they unlock the second sword area in at least one place.
Alternately, maybe completing the first chapter (and seeing the cutscene with the green glowing orb) rewards a token. Possibly just the first time, but I don't think up to four would actually hurt. It would be a little hard on newbies, given the grinding taken to be able to get there, but would help with potential concerns.
Eventually, we'll all have tons of wolves and there will be cheap wolves and perpetual giveaways, but I think it would be good for newbies to have a guaranteed third wolf to help them out. And it'll be nice for those who don't want to interact with the rest of the site, too. The token will be account-bound and cannot be sold, and can be redeemed from the inventory so absolutely zero RNG is involved.
If we're concerned about fairness to older players and stuff, they could also receive 1-4 tokens (depending on implementation) if they've completed the first chapter, or automatically make it so everyone has to redo the glowing orb cutscene if that's required to appropriately distribute the tokens. Personally, I'm not concerned about it, but I could see potential issues arising as a result of not making sure everyone gets it.
I think this would also help with people's frustrations about wolf encounters, and sometimes horrible luck, and would make things a lot more newbie friendly for the future! So everyone can have at least one extra wolf early on.