What speed do you have on your Spectrum service.. because you MUST use a router here. You cannot use a switch between the modem (assuming it is not a router.. ie it will have a single ethernet port) and google wifi which you probably now have setup as main router.
This ancient airport is really inadequate for faster connections than about 200Mbps.
Note the A1143 has two versions.. original one with 100mbit and later one with gigabit ports. Don't even bother if it is the 100mbit.
So if your A1143 is gigabit.. plug it in WAN port to the modem.. LAN port to the mini.
Open the airport utility on your Mac.
1. Reset the airport to factory.
You can do this via the airport utility.. click the icon of the airport in the utility.. and click edit button on the summary page. Go to the top menu and select.. Restore Default Settings

Or do it manually.
Hold in the reset button on the AE and then plug in power.. keep holding in reset for about 10sec until the front led flashes rapidly.. release the button.. wait for the AE to come back up and you will see in the airport utility the white box will have Other Wi-Fi Devices (1)
Click it to do the setup.
2. The setup wizard will start and you can give the AE a suitable name.. eg AE and turn off the wireless.
Everything else should be fine.
Update the AE.
3. Power cycle the modem.. and AE.
At this point you will need to shut down the cable modem for about 15min .. Then power up again. This is required because you are changing routers.
4. Plug the google wifi into AE and reconfigure it to WAP only.