Mount Olympus isn't too high in elevation so it wouldn't be too hard for an ancient greek to climb it if they wanted to. Are there stories of anyone climbing it, was it an off limits zone or anything like that?
More can always be said on the matter, as no answer is ever 'final'; further answers are more than welcome from anyone able to contribute.
For the meantime, OP, you may be interested in the following previous answers on the matter of That Greek Mountain: