Is speed genetic or can it be trained?

Both. Genetics set a large part of your ceiling through muscle fibre composition, limb proportions, and tendon properties. Training still produces substantial improvement in nearly everyone, particularly in acceleration, technique, and strength.

What genetics contribute

Fibre type distribution: A higher proportion of fast-twitch fibres favours rapid force production, and the distribution is largely inherited.
Tendon properties: Achilles length and stiffness influence how efficiently elastic energy is stored and returned.
Limb proportions and joint structure: These shape mechanical advantage and stride characteristics.
Neural characteristics: How quickly and completely you can recruit motor units varies between people.

This is why elite sprinting is one of the least democratic athletic pursuits. Reaching the very top requires a favourable starting point that training cannot manufacture.

What training reliably improves

Almost everyone can get meaningfully faster than they currently are. Acceleration responds particularly well, because it depends heavily on strength and technique. Sprint mechanics can usually be cleaned up substantially. Strength and reactive qualities are trainable in everyone. For a team-sport athlete, these improvements matter far more than a theoretical ceiling.

Realistic scale of change

An untrained person with structured sprint work, strength training, and technique coaching can often improve short-sprint times by a meaningful margin over a year. Highly trained sprinters fight for hundredths. The closer you already are to your ceiling, the smaller the returns.

The practical implication

Genetics decide who wins Olympic finals. They do not decide whether structured training is worth your time. Sprint regularly at high intent, get stronger, train the reactive qualities, and improve your mechanics. The gap between your current speed and your personal ceiling is almost always larger than people assume.