Is there anyway to know if a backup exists from a week ago to restore my phone to without resetting the phone?

Good, forward-thinking question.

Based on your question, you’ve presumably not been backing-up to a Mac … ???

Note that restoring from an iCloud backup is an “all in” proposition which DOES require resetting the phone.

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Also if you were using iCloud Photos, they are generally excluded from backups.

What does iCloud back up? - Apple Support

So … that leaves iCloud Backups.

Look in:

Settings -> Apple Account [Name] -> iCloud -> iCloud Backups.

I think the answer to your question is, "No." I've never restored my phone for fun, only when buying a new one, and I'm sorry that I didn't pay more attention. So I'm not exactly sure how it works. but I'm pretty sure that the only way you can see dates of backups is with a freshly reset phone. That's what this says:

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support 

(which I see that Chattanoogan included earlier.)

Do you think a phone store would let you try it out on a new phone?

If you mean do an “experimental restore”

on a phone in the store … maybe.

That’s a significant “favor” … but you can always ask.

They very well may suspect that you’re attempting some sort of fraud.

The worst they can say is, “Sorry, no.”

HOWEVER, if they say “yes” … all of your account info will then be on that phone.

So you must ensure that you “wipe” the phone afterward. And if you don’t perform all the steps, the phone will be Activation Locked and unable to be used by anyone else.

See how to wipe it here.

What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

If you had an iCloud backup available, you’d see something like this: