I am on day 3 of hardening my cucumber seedling. They were initially out today when it was overcast and then is suddenly turned sunny and I went to check on them after about 45 mins of on and off sun and realized that some of them had leaves that were turning white and drying up (browner folding on the edges), same with one of my eggplants. My squash, tomatoes, herbs and everything else look okay. There was plenty of water in the pots (I had watered them before they went outside). Will those ones survive and what caused them to do this?
Hardening off needs to be done gradually. IMO, that's especially the case with some cucurbits (such as watermelons, and I imagine possibly cucumbers, too).
They weren't introduced to the sun gradually enough, and that's why they got sunscald. It's best to start hardening off plants in the shade.
It sounds like they got too much sun at once, without enough preparation to receive it.
They might survive (sometimes they do; sometimes they don't, and it's especially hard to say without a picture), but I wouldn't count on it.
Cucumbers sprout pretty quickly and easily. So, if it's already warm enough outside at night, I'd take Maxine's advice and plant some more from seed (either directly in their final destination, or in containers outside in full sun). New seedlings that sprout in full sun aren't bothered by it, so you wouldn't even need to worry about hardening those off.
In fact, I don't recommend starting cucurbits indoors at all. They're easier to start outside when it warms up, whether or not you're going to transplant them. I start my cucurbits in foam cups around the time it's warm enough for to plant them directly in the garden, and then I transplant them when they have a few leaves (this works better than direct-seeding for me, since direct-seeded plants get a slower start and don't always germinate well compared to those planted in foam cups to be transplanted later).
Plants lose moisture through transpiration, which occurs through the stomata in the leaves, which open when the sun in strong. (The plans are following the advice, "Make hay while the sun shines.")
Therefore, I like to protect transplants initially from direct sun, especially in the hours of strongest sun.
This is in addition to the sunburn (sunscald) issue.
If the little pots are small, then the water metabolism of the plant is especially vulnerable.
I think it's best to think about two separate aspects of preparing transplants for setting out in the garden:
getting used to the pre-dawn cold temperatures
getting used to the strong sun
Slow and steady wins the race!