Sandy bridge mobo - any chance to upgrade bios having only ivy cpu?

no. it simply wont work.

your 3 options are:
1) get ahold of a sandybridge cpu temporarily.
2) contact gigabyte and ask them to mail you an updated bios for that motherboard (it comes on a chip you replace with the one already there.)
3) send the motherboard back and get a different one which supports ivybridge right out of the box.

Is there any chance that I got a version with updated bios?

From Gigabyte:
The manufacture date can be verified by the serial number found on the product. The first four digits after "SN" determine the year and week of manufacturing date. For example:
"4719331822101 SN082540084966" represents the 25th week of 2008

Check the manufacture date, then check here http://www.gigabyte.com/products/product-page.aspx?pid=...
what BIOS version was available at that date. That would most probably be the board's BIOS version.

Well so it looks like the bios with ivy support was out at 14.10.2011 and my mobo was produced between 17-23.10.2011. So I guess there is a little chance.

Then I suggest waiting for the CPU, install it and test with the board outside the case and a minimum configuration.
There are chances that the CPU is supported.