Any way to check the history of Steam profiles?

Only way I can think of is to check cached version of their profile page on Google (or wayback machine or something similar)

As mentioned, Wayback is the best option, but be aware it won't have archives of all profiles. Best of luck with your plan.

Some of the users write fake country info in their profiles, like Vatican or some Islands, the only way to check real country - steamgifts base of IPs (or their steam reviews on national languages).

Do a region locked giveaway, SG detects their country and won't show them the giveaway even if they lie when they join your group.

The flag people can put on their profiles is meaningless.
e.g. I have the Chinese flag on mine since I live there, and I have a USA region Steam account.

This would require the logs showing what IPs they used to access Steam with. And that info would be super sensitive and I think acquiring it would also break many laws.
Not to mention there are people who regularly access Steam from different IPs. I actually could switch between Hungary and Sweden any time, I access Steam so often from both IP regions. My secondary also has Japan as an offered region.

You can ask for their driving licenses with a timestamp, a certifcation signed by their local mayor and to send you a couple of cotton swabs with their saliva.
OR you could set up a website, invite them there and log their ip, but it's not a foolproof solution either.

Just ask them ^^ Maybe in a massive poll way, and then add needed regions? =P
I can tell that I'm from Kazakhstan so I'm not fitting to any giveaways you are planning to do xD

Is see that there are already good suggestions. (Wayback machine on archive.org or tracking IPs)

Problem with archive.org:
Some users are already using a fake country just for fun.

Problem with IP tracking:
Some users are hidden behind proxies.

Another solution/guess:
It may be much work but you could ask users for a photo that shows a regional newspaper and has their Steam-url ID written on it. It would be important to see the day and city/region from that newspaper.

Every system has its flaws, you need to decide.