"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"
"(? pronoun) meet at the park soon" actually doesn't really make sense due to "meet" being present tense and "soon" indicating something in the future but not in the present. I think in English when we say "I meet at the park soon" what we really mean is "I will meet at the park soon" but since we know due to "soon" it's in the future we swallow the "will" part explicitly indicating future tense. I imagine something similar is happening here in Korean.