For $100 or more you can get it, but you need power of attorney from a notary from both your passport issuer country and Georgia, send a certified copy and so on... which IMO sucks if you hate paperwork and dealing with the old school guys.
Flying there is not that expensive unless you are in South America or Southern Asia. You can have your personal bank account open in 30 minutes in Tbilisi. It's the best banking experience ever (besides fintech).
For banking, I recommend TBC. Big bank, easy to setup, good customer support, easy to use mobile app and digital banking.