A familiar is not random and from what I've experienced, isn't something that can or should be summoned before it's ready to be part of your life.
When it's time to meet your familiar, it will come along. Be it a stray cat who won't leave your house, a stray dog following you around, an animal at the pound that you can't walk away from, a animal given to you by someone else, ect.
When it's time, it's time. Don't rush it or try to find a substitute. They are there to guide and aid us when our souls are ready to learn the lessons their souls teach us.