The question here is really "Are there third-party lenses which will work on the Nikon D3300?", which is only answered by the other "possible duplicate" question in passing, because it starts from the assumption of incompatible mount, when actually third-party manufacturers do produce Nikon-mount lenses — although Sony and Canon do not. (Sigma is the only company I am aware of which makes lenses for their own system and for others.)
So the basic answer is yes — look for lenses from Sigma, Tokina, Tamron, Voigtländer, Zeiss, Samyang, and others which are labeled as for Nikon or F-mount. Note that some of these may be manual focus only, both at the high end (Zeiss, Voigtländer) and budget end (Samyang). And also be aware that these are generally reverse-engineered for compatibility, not licensed, so for lenses which contain electronics, updates may be needed for compatibility in the future.