I got an email stating that the refund will be provided, how long will it take for the refund to show up on my bank account?

I can't tell since I have never asked for a refund, but I believe it should be stated clearly in the email, it would be odd otherwise.
Here's an excerpt from GOG:
Cash refunds can take a few business days, depending on the exact payment method used, your bank, etc. There are some exceptions, such as paysafecard, SOFORT, and GiroPay - for technical reasons, these transactions need to be fully processed before they can be refunded; this can take up to a few weeks.

My guess would be a few business days, 2-4 most likely. At least that's the normal around here.

As that message notes, it would depend on the method you used for payment and how long ago you made the purchase.

If you used a method (e.g. a paper check) that takes a while for the actual underlying $$ payment to come through, any smart vendor is going to sit on a refund until they receive the actual $$ behind the payment - if they don't do that they've got an open invitation for transaction fraud because the initial transaction by itself is more a promise of money than actual money.

That's the mechanism a lot of internet scams use: "Please deposit my $5,000 transaction that takes weeks to validate and I just need you to send me a small chunk of that back in a way that's validated before you figure out you've been scammed!""

If you used a credit card, that is comparatively quick and straight forward.

Most of the time my first choice is card payment. For example, I had Amazon refunds go through in a couple of days, although I noticed they favor in-store credit more often than not.
I have never asked for a game refund since I haven't felt the need to do so, but I would expect the process to be straightforward when it comes to card payments. Other methods take a little bit longer and it makes sense for that to happen.
What puzzles me is the fact that there is no mention of time frame in the email OP received.

You just created your account, and already ask for a refound? Are you here to try to scam GOG?