Apply query arguments after the nth post

Sure! There are tons of parameters for WP-Query that can probably do what you want.

Offset is usually used when your data is ordered. So if you want to ignore the two most recent ones you need to order it by date descending first, then set offset = 2. It doesn’t matter if you apply any other query parameters you have before or after the date thing – you don’t need to do the offset first and then do a second query with other parameters.

You can also add other arguments to the same query if you want it to do something more complicated at the same time, which will apply to all of the results (before and after the offset, which is ok). E.g. search for a search time or choose something in particular category or anything else. But ordering by date is what will help you skip past e.g. the 2 most recent.

Here’s how you do that:

$args = array(
    // order by date
    'orderby' => 'date',
    'order'   => 'DESC',  // descending dates will give you most recent first

    // any extra stuff you want, e.g. search for posts with 'car' but not 'red'
    's' => 'car -red',

    // display posts from the 3rd one onwards, so with date order this will skip two most recent
    'offset' => 2
);

$query = new WP_Query( $args );

If you have a more complicated query you want to do please post more details!