No, it is impossible to beat yourself in Tic Tac Toe.
When I was young, my father taught me Tic Tac Toe. Tic Tac Toe is a game played between two players on a 3×3 square board and has been around for thousands of years. Tic Tac Toe is infinite in the sense that there is an infinite number of games that can be played with only two players. It may seem like no big deal to have access to an infinite number of games, but it means that playing Tic Tac Toe is impossible. Not because Tic Tac Toe is too complicated or challenging, but because Tic Tack Toe cannot be won under any circumstance.
On a 3×3 square board, you must always play first. This means that Tic Tac Toe is a game you cannot win because the other player will always be able to counter your move, and put you in a position where Tic Tac Toe cannot continue. Tic Tac Toe is not a game of strategy or skill – it is a game of luck. You may never lose Tic Tac Toe, but you can never win at it either.