Legally, there is no way to bet on sports without an ID because the minimum age in all states is either 18 or 21 years old.
Whether the age limit is 18 or 21, you'll likely be asked to show identification at a physical sportsbook or casino. For online operators like DraftKings and FanDuel, they require the last four digits of your social security number in order to create an account. For a withdrawal, you'll need to supply a W-9 form no matter how much money you take out.
In person, casinos will check for IDs at the door and if you don't look of age at a sportsbook, you will be asked for ID when making a bet, similar to buying alcohol at a bar. Given that there is an age limit for sports betting no matter where you live, you'll need identification to partake in sports betting. Even if you get away with it and win a decent chunk of money at a sportsbook, you'll need identification and a social security number because winnings above $600 are taxed.
While you may find some places where you can bet without an ID, you're unlikely to be allowed to withdraw money without identification or a SSN.