You don't have to convince them to allow you to do anything; you just have to explain the options to them and let them choose:
(a) you open ports X, Y and Z and then you will be able to access the data using steps 1, 2, 3; otherwise:
(b) you leave the ports closed and have to use steps 4, 5, 6, 7, 8, etc. to access the data.
Alternatively, (b) might be something like: you leave the ports closed, and you can only perform steps 1, 2, 3 from the office; you won't be able to perform them remotely.
Obviously if there are security implications to opening ports X, Y and Z you will want to explain that up front. Otherwise their IT person will explain it to them, and that will make you look bad. You might also want to evaluate the situation and make sure it's actually reasonable to open those ports.
You could also offer alternatives if they want (a) but don't want to open the ports;
(c) you can buy/rent a second server and run it outside the firewall
(d) you can set up a VPN
| This firewall prevents anyone from the outside world (not on the local area) to not be able to pull data from the DBs to put into an Excel sheet. |
This sentence doesn't make a lot of sense to me; a firewall wouldn't be aware of whether the data is being put into an Excel sheet or not. Are you looking to just open the database server port to the outside?