When I search in Preview using cmd+F, I am redirected to the first page of the document. However, many times I am just trying to find the nearest appearance of a word inside the page I am reading. Is there a way to go around this?
I always hate being the bearer of bad news but unfortunately this is the expected behaviour of the Preview application and there is no setting to change it.
Some 3rd party PDF viewers do include the functionality that you're looking for though. May I suggest one called Adobe Acrobat Reader? It does exactly what you want it to do by default (without having to mess with any settings), it's by a reputable software company, and it's free. I just double-checked to make sure it still functions the way I remember and current page searches are working flawlessly for me.
Note: If you remember to set it as your default PDF viewer after installing it (it will prompt you) it will also automatically open each time you attempt to open a PDF file; no fumbling for the right application every time!