Definitely when they hatch, because as soon as they hatch they have to run for their lives and they're immediately in danger. The distance from the where they hatch to the water is pretty long for them to run. They are also exposed and are easy prey for seagulls and crabs. Out of hundreds of eggs, only about 5 to 10 actually survive and get to grow up and mate.
Probably when it's an egg buried in the sand. Since the mother turtle leaves after laying and burying them, they're unprotected. Any predator that comes across them will think "nice ... Conveniently packaged drink boxes."
The next most vulnerable is when they hatch, as they have to dig themselves out and then haul themselves to the water before the sun comes up, or they'll probably cook.
When they first hatch, because they're mother is not with them, 50 come out of of the eggs, but only a few of them live to adult hood, because the walk to the water is dangerous. You see, birds can scoop them up and eat them.
*** soon as the baby turtles start hatching. the most dangerous part of their life is making their way from their nest to the ocean.
Even after they hatch and make it to the water, they're still not safe. Octopus and fish will eat them.
when the females go on the beach to lay their eggs