Here's a different take on it.
Do they actually need the whole data at once? Or are we talking about say, 50 GB *archived* data? If it's just archive, then it's a matter of moving them out into .csv files and storing them on a backup medium, leaving the business with only the active data they are working on for this moment.
Even if they did need more than 2 GB of active data, it now goes to what has already been stated- if it's that essential and huge, then the business will have to cough up the dough to support it. They don't have to hire a full time DBA and a 32 GB, 10UB RAID array octo-core server with Oracle installed to do that; it can be just a small step upward such as signing up with a hosting company that provides a shared database and allowing Access to manage the access to the shared database server.
Even though 2 GB is quite miniscule in grand scheme of things, but when looking at it as a desktop application for storing text and numbers, it's more than aplenty.