I’d put money of the chances that your neighbour is partly parking on common property and I’d double my bet that you have a by-law that says that’s not allowed.
So I’d be asking him politely if there’s anythng he can do to make access easier for you. If he isn’t interested, you can ask the EC or strata manager to issue a Notice To Comply with the by-laws regarding parking on CP.
Your strata plan drawings should show the boundary between private property and common property as a thick black line, just so you are clear you are on solid ground with this. However, if both garages are common property (as they may well be) then there are a whole lot of other issues about appropriate use that may come into play.
By the way, would it make a difference if you swapped sides? That could save everyone a lot of grief.