Just play the lottery and it will up the pet's slvl upon doing so

As for finding eggs more easily, I can say the most effective method is probably just to join the discord if you have one. (You'll need to be verified to see the channels but Takkju or I can take care of that.) There's a userpage share channel where people will usually say when they need eggs hatched. It's slightly more effective but it works.

@Dreamcrystal

@Dreamcrystal

When people have pets that are not out on hoards, it'll appear on people's userpages right above their pets. (When they are on hoards, it just says that in the below screenshot, but that's where it is)