First you need to buy scout from the Gatherer's Gardens, the Scout plasmid will be available to purchase when you reach Siren Alley.

Once you obtain Scout, find the closest Gene Bank.

Switch to Scout, use it and right before you actually enter scout mode, go in the Gene Bank and switch out Scout for any other plasmid.

Exit the Gene Bank, and you will still be in scout mode, press B to return to your body.

If done correctly, you will be invincible. But if you go on to the next main area of the game or put a little sister down to let her obtain adam, you will lose the invincibility.