Create an isochrone map (https://en.wikipedia.org/wiki/Isochrone_map), get a polygon of all the points accessible within N units of time.
An isochrone map basically looks like this (3 isochrones are represented in this example):
Let's just focus on the red one, which takes a center point and a time (or a distance). Based on this time/distance limit, the road network is tested to find all destinations within this limit. This kind of map is often used in marketing/logistics as you can determine which of your customers/warehouse/whatever is accessible within X minutes, so that you can target a specific audience.
The result of the calculation is a polygon (the red polygon for instance, or red+yellow+green).
Then by definition, every node which does not intersect this polygon will be at least N units of time away
There are multiple ways to calculate isochrones (or "isodistance" if you are working with distance limits), but this is a broader question. Also if you don't own the data, some web services will allow you to calculate isochrones worldwide.
The OP seem to have its own road network to work with, so an algorithm will need to be implemented to calculate the isochrone in the first place.
The OSM wiki has some interesting links: