It is of course possible the injector is defect.
You don’t have another one available (or POE out from switch or so) to test ? The device is 802.3af/at compliant so no worries there.
While keeping the injector on port 1, you could try to connect your PC to port2 to see if you can get connection then ?
The led turning green on the LTE does not necessarily mean it has connection. Since you never entered the device, it hasn’t been configured yet so would be strange it can connect out of the box.
Already tried reset ?
Unplug power, press reset and hold while re-applying power (ok, from experience, this can be challenge if you do this alone …).
Hold for 5 sec until the led on the board starts flashing. Then release reset.
If you’re new to Mikrotik, the POE-IN/ether1 port is a WAN port… Even though the WAN is typically LTE for SXT-LTE6, it still support an ethernet internet on ether1. So you won’t get an IP address from ether1 (since it’s listen for one from an ISP)… and winbox discovery will be blocked so it won’t show up as Neighbor. To see if bad injector, leave the injector to power it, but use ether2 to connect to it & see if that works.
@holvoetn, your probably correct BUT I’ve seen the defaults not be quite right in past (e.g. one of the LtAP’s uses a default with ether1 as WAN)…
If OP used QuickSet to change IP, there have been various bugs, including one where DHCP pool was updating correctly. Maybe reset to default be a good way to get out of the current state. To do this, unplug the power, push reset button inside, plug in power again while holding button for ~7 seconds (or until when one light starts flashing) & it will reboot with defaults.