You just bought a network device which is already configured with a static IP, and you don't know what it is. This is how you can find it.
I had to do this recently when I bought an APC Network card which would not factory reset. This means it wouldn't switch back to DHCP, and I needed to find the IP address
First you need to find the mac address. Most devices will have a sticker stating the mac address. If it doesn't, plug it into your managed switch and go take a look at the address table, and get the mac address
Now that you have the mac address, confirm its the device you are looking for by looking up the mac address online. We can see that this device is made by APC, so its the correct mac address
Now, fire up Wireshark on your laptop and filter the packets to only show packets from the mac address of your device. To do this, under the following in the filter field
eth.addr == 00:00:00:00:00:00
Thankfully, this device is broadcasting ARP packets trying to find 22.214.171.124, whatever that may be. From these packets, we can see that our device is 126.96.36.199. Perfect!
From here, you can configure a static IP on your computer so you can talk to it. I decided to set my IP to 188.8.131.52, since we know there shouldn't be any firewalling or blocking to that address on the device since its trying to talk to it already.
Once I did that, bingo! I can get to the login page.