"let's" normally uses the form 합시다. this sentence without context could mean several things, including "(? pronoun) meet at the park soon," "(usually) meet at the park soon" ... if you want to emphasise the "let's" and "soon" it sounds more natural to me to say "우리 빨리 공원에서 만나자" or "우리 빨리 공원에서 만납시다"
That is if you are using deferential speech. 합니다/합니까/합시다/하십시오 have the exact same meanings as the polite mood 해요/해요?/해요/해요. Using only polite speech, I would assume that it is a proposal because it does not have a subject as you pointed out.