So, it's not possible to just come upon your Familiar? From my research so far, I read that a Familiar comes into your life by chance, and they like to hang around your Wiccan materials.
Just two aspects that fit my cat, Petra. About 2 years ago, 2 days after one of my other elderly cats passed away. This kitten just shows up in our yard, literally out of nowhere. No family to be seen anywhere, which was extremely odd. One, lone kitten, by itself, about 8 weeks old. I was able to pick her up by hand, and bring her right inside.
She also lays next to the trunk where I store my portable altar and tools, and especially loves my Bastet statue. She is constantly marking the trunk with the side of her face, as well as my tools. She is very persistant, and she will often times make things somewhat difficult for me when I am preparing things for a blessing, etc.
She really does feel like my Familiar because not long after she appeared, I started slowly looking into the Wiccan religion, like she was encouraging me to do so.