May I wish you a warm welcome to the CameraLabs forum. As a recent convert to m4/3rds I'm not really best placed to offer an answer but here goes...
With no native 300mm m4/3rds prime I'm assuming that manual focus is the order of the day and that opens up a whole world of legacy glass provided you can source a suitable adaptor. But, as I've already discovered, trying to sort the wheat from the chaff can be a problem as most such glass often doesn't benefit from Internet reviews. For example, the LCE currently has an Olympus ZUIKO 300mm OM 1:4.5
for sale for £190. The lens may be marked as in "Good Condition" but was it ever optically good enough for today's digital sensors?
Hugely cheaper than the f/2.8 alternatives so it might be worth a punt if you can find out any more about it?