You don't say why your Echo "cannot connect the Echo to the institute's wifi"? There is certainly no reason to have your Mobile in any local proximity to your Echo. The mobile-phone and Alexa app is only used for the initial set-up of the connection to the wi-fi. After that, it not required to be local.
If you have the password for the institute's Wi-Fi you should be able to connect in the Alexa app by going to Alexa Devices > (Device Name) > Change next to Wi-Fi Network.
If that doesn't help, make sure you're using the latest version of the Alexa app and restart your Echo device. If the issue persists, let us know a few more details, such as any error messages you see or hear and what color the light ring is on your Echo during setup.
My interpretation of the original post is that they do not have permission to connect to the the institute's wifi, perhaps for security reasons. They are looking for other ways of connecting the echo to the internet.
I don't think leaving your phone in the building for extended periods will work, because my experience with personal hot spots is that after a while they drop the WiFi connection, usually after a period of inactivity. You would have to constantly return to make sure it is still working.
The only other option I can think of is a WiFi router with a 4G connection and perhaps a pay as you go SIM card in the router. Unless you can borrow one it will incur additional cost.