Is it possible to have tooth infection without pain?

Unfortunately, Yes!: There are at least two different kinds of dental infections that go can go unnoticed. Periodontal disease is an infection of the gums and bone, that after the initial discomfort, can get much worse, but not feel as bad. Almost half the time a tooth needs a root canal treatment, the abcess will show up on a x-ray without the patient knowing it is there. Both are great reasons for preventive care.

Yes: Very possible. Sometimes a tooth can be infected and have a cavity and no pain is felt. See a dentist asap to get the tooth treated.

Absolutely: There are many infections that take time to cause symptoms and\or be noticed, whether it is related to the teeth or some other part of your mouth or body. These infections may be chronic and dormant or just developing, until they become acute and cause pain.