Ever heard of the Internet? You're company should try storing documents on it

Your* OP is not company :P

The company was dismantled by Michael scofield, so he definitely can't be company.

Yay for Prison Break references!!

Lol that was autocorrect

Storing business documents on the Internet is a dumb idea.

storing business documents on the internet is a really fucking bad idea; but if you store them onto a desktop without using the internet, it's relatively safer (although, paper is the safest option as it cannot be hacked and has the ability to be disposed of in a safe manner; OP's story shows a lack of responsibility with such documents (on the company's part), which shows the fatal flaw with this form of document managing)

My place of employment has things stored on a server - it's a very large company with numerous locations all over the US - and someone from HR at the headquartered location accidentally deleted the information of 500 employees. And, yes, I was one of them.

Just make up a close approximation. No one is going to notice.

Always keep a record for yourself. Either make a copy or put the info on your phone or computer

It's strange that they don't keep at least one other copy if they're sticking to paper time sheets. Take a photo of your sheets and keep it on your phone in case this happens again. It may also be in your (and your company's) best interest to suggest an online scheduling system like Hot Schedules or something if budgeting allows.

I forget what I did 5 minutes ago, so I always keep note as to what project I'm working on for how long each day, say 9:40am to 11am before I do something else. It helps a lot. Get a notepad and just note it down.

Time to make it up realistically!

Encourage your company to do so electronically. Sorry op, I know it can be a pain. Try noting down things you did in a diary. That worked for me when I needed to fill in time sheets from a week or two in the past.

50 hour weeks! Say I have no idea, but you can't under pay me if they ask.

The lack of organization there should raise a red flag to you. Be careful and keep a log of everything you do. Good luck.

next time take pictures of them for reference. thats what i would do in case anything came back incorrectly.