It is the only part of the body without a blood supply. Instead, it receives nutrients via aqueous humor (the liquid between the cornea and vitreous).

Instead, oxygen dissolves in tears and then diffuses throughout the cornea to keep it healthy.[5] Similarly, nutrients are transported via diffusion from the tear fluid through the outside surface and the aqueous humour through the inside surface.

And because that seemed lacking still and I’m too dumb to figure it out ChatGPT’s response:

The palpebral conjunctival blood vessels and the capillaries of the eyelids supply oxygen to the tear film behind closed lids. Oxygen diffuses from these vessels into the cornea.