Well, one way or another the HomePod requires a WiFi connection to operate. It doesn’t necessarily need internet, depending on how you’re going to use it in the short term until things are back to normal.
You have two options, I’ll list the easiest first;
1) Assuming you will be using the same router in your new home as you did in your old one.
Just power up that router (it doesn’t need to be connected to the internet in any way for this). Your HomePod will automatically connect to it as that’s what it was connected to in your old home.
Any music you want to listen to, just download onto your iPhone, or iPad, for offline listening.
Connect your iPhone or iPad to the same WiFi connection your HomePod is on (again no internet needed) and just AirPlay your music directly to the HomePod.
That’s the easy way in the short term as it doesn’t require you to change anything.
2) This method does require the HomePod to be setup from scratch again now. And then again once your home internet is connected.
Using your iPhone as a hotspot, connect both the HomePod and the iPad to that hotspot. Setup the HomePod from scratch and just use it normally so long as it’s connected to the hotspot.
One way around having to setup the HomePod from scratch, is to give your iPhone (temporarily if you like) the same SSID and password as the router you normally connect to.
To do that go to Settings > General > About > Name and rename your iPhone to the SSID your router uses.
Then go to Settings > Personal Hotspot > WiFi Password and change that to the password your router uses.
Now when you enable the hotspot on your iPhone, your HomePod should automatically connect to it as it has the matching details it’s looking for.