Device without GW (and static route option) needs to connect to another network

Hi all,

I have a challenge with an alarm system that should connect to another subnet behind L2L VPN but it does not have a gateway in LAN.

Network diagram: https://imgur.com/a/zPrXSb0

Alarm system has two network cards.

First one is connected to local LAN (192.168.0.0/24) without gateway. Second one is connected to vendors LTE router to enable remote management for them. This network card has the default GW.

Now additionally to LAN access this alarm system has a new need to connect to another site (192.168.1.0/24) through L2L VPN.

Unfortunately system is locked and static routes cannot be added to it so default gateway points traffic to wrong direction.

I'm drawing a blank here. Can anything be done with the local firewall (ASA 5506) to help guide the traffic to right direction?