I thought it took a few sperm to get through the outer shell of the egg before one sperm could fertilize the egg.
Generally the first sperm in creates a change in the egg’s membrane so that no other sperm can enter. If more than one sperm did enter, there would be a high chance of chromosomal abnormalities that might cause fertilization to fail or a spontaneous abortion.
You’re quite right. The egg is quite well protected by its own cell membrane and substances it secretes. Sperm have to digest their way in to the egg using enzymes located in the head, and no individual sperm has near enough enzymes to do this. As a result the first few dozen sperm to arrive deplete their enzymes and die without being able to achieve fertilisation. However they do soften the egg up for later arrivals.
Contrary to popular belife the first sperm to arrive doesn’t fertlise the egg, it dies in a futile attempt to get in. It is the later arrivavls that manage to achieve fertilisation.