I'm pretty new, and I was wondering if there was a list of all the ways available to gain pets slots?

You can buy up to 45 for 2000 CSC each through the Pets page (direct link)

You can buy up to 15 from the Millionaire Center (direct link). These start at 20m sP each and the price increases by 20m per slot up until the 10th (so the 10th slot costs 200m, which is just slightly cheaper than the current SS price of CSC). Then it resets at 20m for the 11th slot and increases in price up to the 15th.

Starting on your second anniversary, you get a loyalty box each year you've been on Subeta and one of the options you can pick from the box is a free pet slot.

And sometimes we'll have site-wide events (we had a Quest-a-Thon recently where we had to do a total of 1,250,000 quests within about two weeks and everyone who participated got the prizes) and sometimes pet slots will be given out through those also

thank you!