The evidence can take a number of different forms: admissions from the mouth of the dog owner, animal control records and police reports establishing a prior bite, statements from neighbors or other witnesses, or veterinarian records if you can get them on the attacking dog.
Those other witnesses can include neighborhood kids, people who walk their dogs in the neighborhood, people who visit the dog park if there is one, mail delivery workers, FedEx and UPS drivers, gardeners if there are any, people who jog or ride bikes down the block, people who wait at a nearby bus stop, and the adjacent neighbors to the north, west, east and south.
To find witnesses, you need to visit animal control, the police station, and the post office. You need to phone the UPS and FedEx offices in the vicinity of the accident. You should create flyers that say you were bitten by a dog that lives at such-and-such an address, or you are a mom or a dad whose child was bitten, and that you desperately need information about the dog in order to pay your medical bills.
Most importantly, you must go to the location of the accident and talk to children, the neighbors and people walking, jogging, biking, delivering, gardening, and working there.
Anyone who gives you favorable information has to be "open" to speak with your attorney. Anonymous witnesses are of little use. You need to obtain names and contact information. If a child seems to have information, get the gist of it but conduct your "interview" in the presence of his mother or father, to avoid any appearance of impropriety and to ensure their cooperation later on.
In my experience, every dog that injures a person seriously has behaved viciously in the past. Therefore you should not give up until you uncover that prior behavior.