If the Church has Internet, that should allow you to create a peer to peer network that all the computers can join. It needs to have a password because you don't want anyone in the church that is using your public internet to be able to access the connected computers.
See if you can get instructions from the church's internet provider. Most people who have more than one computer at home have made a network. I have two desktops and my laptop connected and the printer is also connected so all the computers can use the printer via the network.
I recently created a database for a charity. I did not like the idea of having to install the BE of the application on one of the workstations where a person might or might not be working or even in the office if the workstation was a laptop that could be taken home. So, I also donated an NAS drive. This is the link
https://www.amazon.com/gp/product/B00JKM0A36/ref=ppx_yo_dt_b_asin_title_o02_s00?ie=UTF8&psc=1
It has 2 T of storage and was the perfect solution. It plugs directly into the router - check the router to ensure that it has a usb you can plug into. The drive has enough "intelligence" to act as a file server (DO NOT USE THE CLOUD FEATURE - this must be installed as a local drive with no cloud functionality or Access will not work) I consider it to be a bargain. It was pretty easy to set up. I talked to the charity's IT support and he has moved all their shared files to this drive and he also using some of the space to take backups. The Access app only needed a very tiny space on the drive.
So, if you don't donate or get them to buy a drive like this, you can pick a computer that must always be on when they are working in the office and designate it as the "server". Create a separate folder that you can designate with a drive letter that everyone can link to. The BE goes in the "shared" folder. Then I use a batch file which is run from a shortcut on each desktop to copy the FE from the master folder on the "shared" drive to each user's local drive. So, the FE is replaced each time they open it and it always runs from the local computer.
Access can be flaky when you connect to the LAN wirelessly as you will be doing and as my charity people do. But, sometimes you don't have great technology. You'll have to instruct the users that if there is a network "blip" they might lose their connection. They need to shut the app and then reopen it. They will probably have lost the record they were entering/updating but they can renter it when they reconnect.