OK, I'm going to step back a bit and talk about another elephant in the room.
Access does not work directly over the Internet. PERIOD. It is because the general Internet doesn't work correctly when using the preferred Windows protocol for file and printer sharing. This protocol, Server Message Block (SMB), PRESUMES a permanent and persistent connection over a local area network (LAN) - which is NOT the Internet. SMB is the backbone of Access and, since we don't have OpenSource Access, we cannot change the SMB protocol for something else more suited to Internet communications. Though there are newer versions of SMB, they still have the Internet incompatibility issue. Therefore, the simplest answer is "No LAN? No Access!"
So-called cloud solutions will depend on a lot of factors, but most of the common commercial "cloud" setups do not honor SMB protocol either. For that reason, direct cloud-based solutions so rarely work correctly as to say "No" again. Though there are a few situations where something like a cloud solution actually CAN be made to work within limits.
It's not TOTALLY impossible, however. You can do some things with Azure and a few other file storage systems. We have people here who have looked into storing tables under control of Azure and using Access. I'll have to step away and just let them comment as they see fit because I've never used Azure myself.
You can also look into using RDP (Remote Datagram Protocol) or CITRIX as ways to use the web to open a channel to a central system, after which you can do some things via RDP or CITRIX. You need a system to act as a server for either option, and CITRIX is not cheap. The license to run Access also could become an issue since remote-hosting setups usually run Access on the host system, which therefore needs an Access mutli-user license. Our member Pat Hartman has considerable experience with CITRIX. You also need a decent IT support staff if you go that way, since it is quite common for an IT person to incorrectly configure RDP or CITRIX if they don't understand Access requirements.
If you don't have an appropriate server, then the only other possible solution is to pick some kind of transaction file that you have each user export to become a separate file. Then you can use something like FTP to allow the transaction file to be transmitted to your central data repository, whatever that is. Then you read and work with the transaction files to apply them appropriately. If transactions have to go back down to the individual users, you create another transaction file, FTP it to the end users, and have a facility in these separate databases to import the downloads. If you go this way, users CANNOT be allowed to 'fiddle' with the format. Otherwise, the whole scheme goes down the toilet.
Sounds ugly? Yep, totally. The U.S. Navy's transactions with several of the financial offices were in, essentially, big .CSV files sent up or down via FTP on a daily schedule. We talked with 18 different offices from the Reserve Headquarters Support machine, and ALL of them used more or less the same concept - a delimited file with many lines, each long line in that file representing one record. A light day was when the transaction file only had thousands of lines rather than tens of thousands of lines. (Wasn't an Access DB in this case.)