The Lexico example that you quoted in your comment is correct because "over the parking lot" says that the window looks out over the parking lot.
The sentence in your question is not correct because the guy doesn't have a vantage point over the garden- your balcony does, and you do. You usually to use this meaning of over with the verb look rather than see.
You could make your sentence work by changing it like this:
I went out onto the balcony and looked out over the garden, where I saw a rather thin, dark-haired guy.
Note that there is a conventional sequence for adjectives, and size comes before colour, so thin should be before dark haired.