Start by softening the cream cheese for at least 1 hour. When you're ready to cook mince the garlic, (I use a garlic press) then dice the onion and bell pepper.
Next add the ground beef to a large pot and cook breaking it up into small bits. When the meat is partially done and broken up, add the onion and garlic. Cook for 2-3 minutes until the onion is turning translucent.
Simmer until the bell pepper and onions are completely tender, about 10 minutes. If you're using the dairy-free option of unsweetened coconut cream, add it in now so the flavors can simmer together.
Add the softened cream cheese in small chunks, the smaller the chunks, the easier it is to mix in. Stir to combine, let the soup sit then stir a bit more to completely combine the cream cheese.