Only about a quarter of the time. Just 25.9% of first touchdowns are scored on the game's opening possession. The median first touchdown arrives on the game's third drive, 67.2% have been scored by the end of drive four, and 82.5% by drive six.
Related numbers worth knowing: 99.3% of NFL games produce at least one touchdown, the game's first score is a touchdown (rather than a field goal or safety) 59.2% of the time, and the team that receives the opening kickoff scores the game's first touchdown 57.8% of the time, though since the coin toss decides possession, that last edge can't be bet in advance.
For first-TD handicapping, the window that matters is the first four to five drives per team. Players whose usage is concentrated there, scripted-play targets, early-down backs with goal-line roles, carry more equity than their full-game numbers suggest.
Source: 1,087 regular-season NFL games, 2022–2025, official play-by-play. Full method on the methodology page.