To reliably hold a bit over 2GB of data in RAM on AWS, you'll probably need something like a t4g.medium, about $0.0336/hr on-demand. 730 hours in a month, so $24.528, but ideally you'll have like three or so instances so like $74/mo. That's before thinking about stuff like IP address costs, the EBS volumes underpinning those boxes, etc. And then managing all the syncing and what not.

Of course, that's list prices, you can get savings plans and RIs and discounts.

The cost of RAM per hour in AWS isn't cheap.