If you have access to a Linux box you don't need any weird sources of entropy or timestamps. It's already there, securely built in. Simply do:-
dd if=/dev/random of=random_bits bs=1 count=32 iflag=fullblock
after you have been using the machine for a good few minutes. The usage is important as it reads your I/O activities and securely extracts information entropy from it. You'll have 256 bits of excellent entropy in the file called
random_bits. This is the closest you'll get to using a TRNG without separate TRNG hardware The PC is the hardware. The key will be as good as you'll ever see. Then simply hard code within your device. You can see them with:-
Hard coding is very common in retail/consumer devices and there will be several in your home (smart door bell, smart TV, video recorder, pet id etc.) It's not as secure (or complicated) as key exchange, but it'll probably do.
Note that this answer relates specifically to the one off /few key(s) requirement of this question. More frequent key requests may cause /dev/random to block. However, anecdotally I get ~56kbits of output per hour simply dealing with my emails (on Ubuntu 18).